{"id":38507,"date":"2026-05-27T09:01:03","date_gmt":"2026-05-27T09:01:03","guid":{"rendered":"https:\/\/mp.moonpreneur.com\/math-corner\/?p=38507"},"modified":"2026-05-27T17:19:53","modified_gmt":"2026-05-27T17:19:53","slug":"vertex-formula-explained","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/vertex-formula-explained\/","title":{"rendered":"What is the Vertex Formula?"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"38507\" class=\"elementor elementor-38507\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-cf42691 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cf42691\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2ccd261\" data-id=\"2ccd261\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-acf9120 elementor-widget elementor-widget-html\" data-id=\"acf9120\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div class=\"math-card\"> \r\n\r\n  <h2>The Vertex Formula?<\/h2>\r\n\r\n  <label>Adjust b value:<\/label>\r\n  <input type=\"range\" min=\"-20\" max=\"20\" value=\"6\" class=\"slider\" id=\"radiusSlider3\"\/>\r\n\r\n  <div class=\"circle-box\">\r\n    <div class=\"circle\">\r\n\r\n      <div class=\"radius-line\"><\/div>\r\n      <div class=\"center-dot\"><\/div>\r\n\r\n      <div class=\"radius-text\">\r\n        b = <span id=\"r3\">6<\/span>\r\n      <\/div>\r\n\r\n      <div class=\"area-text\">\r\n        x = <span id=\"a3\">-1.5<\/span>\r\n      <\/div>\r\n\r\n    <\/div>\r\n  <\/div>\r\n\r\n  <table>\r\n    <tr>\r\n      <th>Formula<\/th>\r\n      <td>x = -b \/ 2a<\/td>\r\n    <\/tr>\r\n\r\n    <tr>\r\n      <th>a (constant)<\/th>\r\n      <td>2<\/td>\r\n    <\/tr>\r\n\r\n    <tr>\r\n      <th>b value<\/th>\r\n      <td><span id=\"tableR3\">6<\/span><\/td>\r\n    <\/tr>\r\n\r\n    <tr>\r\n      <th>Vertex (x)<\/th>\r\n      <td><span id=\"tableA3\">-1.5<\/span><\/td>\r\n    <\/tr>\r\n  <\/table>\r\n\r\n<\/div>\r\n\r\n<style>\r\n.math-card{\r\n  max-width:500px;\r\n  margin:auto;\r\n  background:#fff;\r\n  padding:20px;\r\n  border-radius:18px;\r\n  box-shadow:0 10px 25px rgba(0,0,0,0.08);\r\n  font-family:Arial,sans-serif;\r\n}\r\n\r\n.slider{\r\n  width:100%;\r\n  margin-bottom:20px;\r\n}\r\n\r\n.circle-box{\r\n  display:flex;\r\n  justify-content:center;\r\n  margin-bottom:20px;\r\n}\r\n\r\n.circle{\r\n  width:180px;\r\n  height:180px;\r\n  border:5px solid #2563eb;\r\n  border-radius:50%;\r\n  position:relative;\r\n  background:rgba(37,99,235,0.08);\r\n}\r\n\r\n.radius-line{\r\n  width:70px;\r\n  height:4px;\r\n  background:#10b981;\r\n  position:absolute;\r\n  top:50%;\r\n  left:50%;\r\n  transform-origin:left center;\r\n  animation:spin 5s linear infinite;\r\n}\r\n\r\n.center-dot{\r\n  width:14px;\r\n  height:14px;\r\n  background:red;\r\n  border-radius:50%;\r\n  position:absolute;\r\n  top:50%;\r\n  left:50%;\r\n  transform:translate(-50%,-50%);\r\n}\r\n\r\n.radius-text{\r\n  position:absolute;\r\n  top:40%;\r\n  left:58%;\r\n  color:#10b981;\r\n  font-weight:bold;\r\n}\r\n\r\n.area-text{\r\n  position:absolute;\r\n  bottom:-28px;\r\n  left:35px;\r\n  color:#7c3aed;\r\n  font-weight:bold;\r\n}\r\n\r\ntable{\r\n  width:100%;\r\n  border-collapse:collapse;\r\n}\r\n\r\ntable th,\r\ntable td{\r\n  border:1px solid #ddd;\r\n  padding:12px;\r\n}\r\n\r\ntable th{\r\n  background:#f3f4f6;\r\n}\r\n\r\n@keyframes spin{\r\n  from{transform:rotate(0deg);}\r\n  to{transform:rotate(360deg);}\r\n}\r\n<\/style>\r\n\r\n<script>\r\nconst slider3 = document.getElementById(\"radiusSlider3\");\r\n\r\n\/\/ fixed a value for accuracy\r\nconst a = 2;\r\n\r\nslider3.oninput = function(){\r\n\r\n  let b = parseFloat(this.value);\r\n\r\n  let vertexX = (-b \/ (2 * a)).toFixed(2);\r\n\r\n  document.getElementById(\"r3\").innerHTML = b;\r\n  document.getElementById(\"a3\").innerHTML = vertexX;\r\n\r\n  document.getElementById(\"tableR3\").innerHTML = b;\r\n  document.getElementById(\"tableA3\").innerHTML = vertexX;\r\n};\r\n<\/script>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-58f24f4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"58f24f4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7f4c3f7\" data-id=\"7f4c3f7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1ac7800 elementor-widget elementor-widget-text-editor\" data-id=\"1ac7800\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Imagine you&#8217;re on a roller coaster. You go up&#8230; up&#8230; up and suddenly &#8211; whoosh\u2014whoosh!\u2014you reach the highest point and start coming down. Or maybe you&#8217;re in a valley, reaching the lowest point before climbing again.<\/span><\/p><p><span style=\"font-weight: 400;\">That special turning point is exactly what we call the vertex in math!<\/span><\/p><p><span style=\"font-weight: 400;\">And guess what? The vertex formula helps us find that magical point quickly and easily.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-386d87e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"386d87e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2bd2118\" data-id=\"2bd2118\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-effac1b elementor-widget elementor-widget-html\" data-id=\"effac1b\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<!DOCTYPE html>\r\n<html lang=\"en\">\r\n<head>\r\n<meta charset=\"UTF-8\"\/>\r\n<title>Vertex Formula Title<\/title>\r\n\r\n<style>\r\n  body {\r\n    margin: 0;\r\n    padding: 0;\r\n    font-family: Arial, sans-serif;\r\n    background: #f4f4f4;\r\n  }\r\n\r\n  .title-container {\r\n    display: flex;\r\n    justify-content: center;\r\n    align-items: center;\r\n    padding: 0px 10px;\r\n  }\r\n\r\n  .title-box {\r\n    position: relative;\r\n    background: linear-gradient(135deg, #7c3aed, #2563eb);\r\n    padding: 10px 10px;\r\n    border-radius: 50px;\r\n    color: #fff;\r\n    text-align: center;\r\n    box-shadow: 0 10px 25px rgba(0,0,0,0.2);\r\n  }\r\n\r\n  \/* Decorative shapes *\/\r\n  .title-box::before,\r\n  .title-box::after {\r\n    content: \"\";\r\n    position: absolute;\r\n    width: px;\r\n    height: px;\r\n    background: #10b981;\r\n    border-radius: 50%;\r\n    top: 50%;\r\n    transform: translateY(-50%);\r\n  }\r\n\r\n  .title-box::before {\r\n    left: -15px;\r\n  }\r\n\r\n  .title-box::after {\r\n    right: -15px;\r\n  }\r\n\r\n  .title-box h2 {\r\n    margin: 0;\r\n    font-size: 34px;\r\n    letter-spacing: 1px;\r\n  }\r\n<\/style>\r\n\r\n<\/head>\r\n<body>\r\n\r\n<div class=\"title-container\">\r\n  <div class=\"title-box\">\r\n    <h3>What is the Vertex Formula?\r\n\r\n  <\/h3><\/div>\r\n<\/div>\r\n\r\n<\/body>\r\n<\/html>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-b379ebd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b379ebd\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ff2c9e2\" data-id=\"ff2c9e2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8f5f930 elementor-widget elementor-widget-text-editor\" data-id=\"8f5f930\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">The Vertex Formula is used to find the exact point where a parabola turns\u2014 this is called the vertex.<\/span><\/p><p><span style=\"font-weight: 400;\">In simple words:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It tells you the highest point (maximum)OR<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The lowest point (minimum) of a curve<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">This is also known as the vertex of a parabola formula.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-d48536f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d48536f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-746c891\" data-id=\"746c891\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b2d877d elementor-widget elementor-widget-html\" data-id=\"b2d877d\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<!DOCTYPE html>\r\n<html lang=\"en\">\r\n<head>\r\n<meta charset=\"UTF-8\"\/>\r\n<title>Vertex Formula Title<\/title>\r\n\r\n<style>\r\n  body {\r\n    margin: 0;\r\n    padding: 0;\r\n    font-family: Arial, sans-serif;\r\n    background: #f4f4f4;\r\n  }\r\n\r\n  .title-container {\r\n    display: flex;\r\n    justify-content: center;\r\n    align-items: center;\r\n    padding: 0px 10px;\r\n  }\r\n\r\n  .title-box {\r\n    position: relative;\r\n    background: linear-gradient(135deg, #7c3aed, #2563eb);\r\n    padding: 20px 40px;\r\n    border-radius: 50px;\r\n    color: #fff;\r\n    text-align: center;\r\n    box-shadow: 0 10px 25px rgba(0,0,0,0.2);\r\n  }\r\n\r\n  \/* Decorative shapes *\/\r\n  .title-box::before,\r\n  .title-box::after {\r\n    content: \"\";\r\n    position: absolute;\r\n    width: px;\r\n    height: px;\r\n    background: #10b981;\r\n    border-radius: 50%;\r\n    top: 50%;\r\n    transform: translateY(-50%);\r\n  }\r\n\r\n  .title-box::before {\r\n    left: -15px;\r\n  }\r\n\r\n  .title-box::after {\r\n    right: -15px;\r\n  }\r\n\r\n  .title-box h1 {\r\n    margin: 0;\r\n    font-size: 34px;\r\n    letter-spacing: 1px;\r\n  }\r\n<\/style>\r\n\r\n<\/head>\r\n<body>\r\n\r\n<div class=\"title-container\">\r\n  <div class=\"title-box\">\r\n    <h4>Standard Form of Parabola\r\n\r\n  <\/h4><\/div>\r\n<\/div>\r\n\r\n<\/body>\r\n<\/html>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-745335b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"745335b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-08f33e0\" data-id=\"08f33e0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a38d8db elementor-widget elementor-widget-text-editor\" data-id=\"a38d8db\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">The basic equation of a parabola is: y=ax\u00b2+bx+c<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">If a &gt;0 \u2192 parabola opens upward (minimum point)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">If a &lt;0 \u2192 parabola opens downward (maximum point)<\/span><\/li><\/ul>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-40e1544 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"40e1544\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e46ab2a\" data-id=\"e46ab2a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ce0ff6d elementor-widget elementor-widget-html\" data-id=\"ce0ff6d\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<!DOCTYPE html>\r\n<html lang=\"en\">\r\n<head>\r\n<meta charset=\"UTF-8\"\/>\r\n<title>Vertex Formula Title<\/title>\r\n\r\n<style>\r\n  body {\r\n    margin: 0;\r\n    padding: 0;\r\n    font-family: Arial, sans-serif;\r\n    background: #f4f4f4;\r\n  }\r\n\r\n  .title-container {\r\n    display: flex;\r\n    justify-content: center;\r\n    align-items: center;\r\n    padding: 0px 10px;\r\n  }\r\n\r\n  .title-box {\r\n    position: relative;\r\n    background: linear-gradient(135deg, #7c3aed, #2563eb);\r\n    padding: 20px 40px;\r\n    border-radius: 50px;\r\n    color: #fff;\r\n    text-align: center;\r\n    box-shadow: 0 10px 25px rgba(0,0,0,0.2);\r\n  }\r\n\r\n  \/* Decorative shapes *\/\r\n  .title-box::before,\r\n  .title-box::after {\r\n    content: \"\";\r\n    position: absolute;\r\n    width: px;\r\n    height: px;\r\n    background: #10b981;\r\n    border-radius: 50%;\r\n    top: 50%;\r\n    transform: translateY(-50%);\r\n  }\r\n\r\n  .title-box::before {\r\n    left: -15px;\r\n  }\r\n\r\n  .title-box::after {\r\n    right: -15px;\r\n  }\r\n\r\n  .title-box h1 {\r\n    margin: 0;\r\n    font-size: 34px;\r\n    letter-spacing: 1px;\r\n  }\r\n<\/style>\r\n\r\n<\/head>\r\n<body>\r\n\r\n<div class=\"title-container\">\r\n  <div class=\"title-box\">\r\n    <h5>Vertex Form Formula\r\n\r\n\r\n  <\/h5><\/div>\r\n<\/div>\r\n\r\n<\/body>\r\n<\/html>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-227feb2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"227feb2\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-14dfb8a\" data-id=\"14dfb8a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a04536d elementor-widget elementor-widget-text-editor\" data-id=\"a04536d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Another way to write the equation is the vertex form formula:<\/span><\/p><p><span style=\"font-weight: 400;\">y=a(x\u2212h)\u00b2 +k<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Here:(h,k) is the vertex<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">This form directly shows the turning point!<\/span><\/li><\/ul>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-92bce6a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"92bce6a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0c6e694\" data-id=\"0c6e694\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-66c541f elementor-widget elementor-widget-html\" data-id=\"66c541f\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<!DOCTYPE html>\r\n<html lang=\"en\">\r\n<head>\r\n<meta charset=\"UTF-8\"\/>\r\n<title>Vertex Formula Box<\/title>\r\n\r\n<style>\r\n  body {\r\n    font-family: Arial, sans-serif;\r\n    background: #f4f4f4;\r\n    padding: 20px;\r\n  }\r\n\r\n  .formula-card {\r\n    max-width: 650px;\r\n    margin: auto;\r\n    background: #ffffff;\r\n    border-radius: 18px;\r\n    box-shadow: 0 10px 25px rgba(0,0,0,0.1);\r\n    padding: 25px;\r\n  }\r\n\r\n  .title {\r\n    text-align: center;\r\n    background: linear-gradient(135deg, #7c3aed, #2563eb);\r\n    color: white;\r\n    padding: 15px;\r\n    border-radius: 12px;\r\n    font-size: 24px;\r\n    margin-bottom: 20px;\r\n  }\r\n\r\n  .formula-box {\r\n    background: #eef2ff;\r\n    padding: 15px;\r\n    border-radius: 12px;\r\n    margin-bottom: 20px;\r\n  }\r\n\r\n  .formula-box h3 {\r\n    margin-top: 0;\r\n    color: #4338ca;\r\n  }\r\n\r\n  .formula {\r\n    font-size: 18px;\r\n    font-weight: bold;\r\n    color: #111827;\r\n    margin: 10px 0;\r\n  }\r\n\r\n  .highlight {\r\n    color: #dc2626;\r\n    font-weight: bold;\r\n  }\r\n\r\n  .steps-box {\r\n    background: #f0fdf4;\r\n    padding: 15px;\r\n    border-radius: 12px;\r\n  }\r\n\r\n  .steps-box h3 {\r\n    margin-top: 0;\r\n    color: #059669;\r\n  }\r\n\r\n  .steps-box p {\r\n    margin: 8px 0;\r\n  }\r\n<\/style>\r\n\r\n<\/head>\r\n<body>\r\n\r\n<div class=\"formula-card\">\r\n\r\n  <div class=\"title\">Vertex of Parabola Formula (Two Methods)<\/div>\r\n\r\n  <div class=\"formula-box\">\r\n    <h3>Formula 1 (Direct Formula)<\/h3>\r\n\r\n    <div class=\"formula\">(h, k) = (-b \/ 2a , -D \/ 4a)<\/div>\r\n\r\n    <p><b>Where:<\/b> D = b\u00b2 \u2212 4ac<\/p>\r\n\r\n    <p class=\"highlight\">This is the most powerful vertex of the parabola formula!<\/p>\r\n  <\/div>\r\n\r\n  <div class=\"steps-box\">\r\n    <h3>Formula 2 (Step-by-Step Method)<\/h3>\r\n\r\n    <p><b>Step 1:<\/b> Find h (x-coordinate)<\/p>\r\n    <p class=\"formula\">h = -b \/ 2a<\/p>\r\n\r\n    <p><b>Step 2:<\/b> Substitute h into the equation to find k<\/p>\r\n\r\n    <p class=\"highlight\">An easy and beginner-friendly way to use the vertex formula!<\/p>\r\n  <\/div>\r\n\r\n<\/div>\r\n\r\n<\/body>\r\n<\/html>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-92a68b7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"92a68b7\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0685be8\" data-id=\"0685be8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-34e51b5 elementor-widget elementor-widget-html\" data-id=\"34e51b5\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<!DOCTYPE html>\r\n<html lang=\"en\">\r\n<head>\r\n<meta charset=\"UTF-8\"\/>\r\n<title>Vertex Formula Title<\/title>\r\n\r\n<style>\r\n  body {\r\n    margin: 0;\r\n    padding: 0;\r\n    font-family: Arial, sans-serif;\r\n    background: #f4f4f4;\r\n  }\r\n\r\n  .title-container {\r\n    display: flex;\r\n    justify-content: center;\r\n    align-items: center;\r\n    padding: 0px 10px;\r\n  }\r\n\r\n  .title-box {\r\n    position: relative;\r\n    background: linear-gradient(135deg, #7c3aed, #2563eb);\r\n    padding: 20px 40px;\r\n    border-radius: 50px;\r\n    color: #fff;\r\n    text-align: center;\r\n    box-shadow: 0 10px 25px rgba(0,0,0,0.2);\r\n  }\r\n\r\n  \/* Decorative shapes *\/\r\n  .title-box::before,\r\n  .title-box::after {\r\n    content: \"\";\r\n    position: absolute;\r\n    width: px;\r\n    height: px;\r\n    background: #10b981;\r\n    border-radius: 50%;\r\n    top: 50%;\r\n    transform: translateY(-50%);\r\n  }\r\n\r\n  .title-box::before {\r\n    left: -15px;\r\n  }\r\n\r\n  .title-box::after {\r\n    right: -15px;\r\n  }\r\n\r\n  .title-box h1 {\r\n    margin: 0;\r\n    font-size: 34px;\r\n    letter-spacing: 1px;\r\n  }\r\n<\/style>\r\n\r\n<\/head>\r\n<body>\r\n\r\n<div class=\"title-container\">\r\n  <div class=\"title-box\">\r\n    <h6>Derivation of Vertex Formula\r\n\r\n\r\n  <\/h6><\/div>\r\n<\/div>\r\n\r\n<\/body>\r\n<\/html>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-97609ee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"97609ee\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2765c9b\" data-id=\"2765c9b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-12dd009 elementor-widget elementor-widget-text-editor\" data-id=\"12dd009\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Let&#8217;s convert the standard form into the vertex formula:<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-889ff16 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"889ff16\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c606a72\" data-id=\"c606a72\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e097c59 elementor-widget elementor-widget-html\" data-id=\"e097c59\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<!DOCTYPE html>\r\n<html lang=\"en\">\r\n<head>\r\n<meta charset=\"UTF-8\"\/>\r\n<title>Vertex Formula Derivation<\/title>\r\n\r\n<style>\r\n  body {\r\n    margin: 0;\r\n    padding: 20px;\r\n    font-family: Arial, sans-serif;\r\n    background: #111827;\r\n  }\r\n\r\n  .derivation-box {\r\n    max-width: 700px;\r\n    margin: auto;\r\n    background: linear-gradient(135deg, #4f46e5, #9333ea);\r\n    border-radius: 20px;\r\n    padding: 25px;\r\n    box-shadow: 0 12px 30px rgba(0,0,0,0.4);\r\n    color: #ffffff;\r\n  }\r\n\r\n  .derivation-box h2 {\r\n    text-align: center;\r\n    margin-bottom: 20px;\r\n    font-size: 26px;\r\n    letter-spacing: 1px;\r\n  }\r\n\r\n  .step {\r\n    background: rgba(255,255,255,0.1);\r\n    border-left: 5px solid #22c55e;\r\n    padding: 15px;\r\n    border-radius: 12px;\r\n    margin-bottom: 15px;\r\n  }\r\n\r\n  .step-title {\r\n    font-weight: bold;\r\n    margin-bottom: 8px;\r\n    color: #facc15;\r\n  }\r\n\r\n  .formula {\r\n    font-family: \"Courier New\", monospace;\r\n    font-size: 16px;\r\n    line-height: 1.6;\r\n  }\r\n\r\n  .final {\r\n    background: rgba(0,0,0,0.3);\r\n    border-left: 5px solid #f43f5e;\r\n  }\r\n\r\n<\/style>\r\n\r\n<\/head>\r\n<body>\r\n\r\n<div class=\"derivation-box\">\r\n\r\n  <h2>Derivation of Vertex Formula (Simplified)<\/h2>\r\n\r\n  <div class=\"step\">\r\n    <div class=\"step-title\">Start with:<\/div>\r\n    <div class=\"formula\">y = ax\u00b2 + bx + c<\/div>\r\n  <\/div>\r\n\r\n  <div class=\"step\">\r\n    <div class=\"step-title\">Step 1: Move Constant<\/div>\r\n    <div class=\"formula\">y \u2212 c = ax\u00b2 + bx<\/div>\r\n  <\/div>\r\n\r\n  <div class=\"step\">\r\n    <div class=\"step-title\">Step 2: Take \"a\" common<\/div>\r\n    <div class=\"formula\">y \u2212 c = a (x\u00b2 + (b\/a)x)<\/div>\r\n  <\/div>\r\n\r\n  <div class=\"step\">\r\n    <div class=\"step-title\">Step 3: Complete the square<\/div>\r\n    <div class=\"formula\">y \u2212 c = a (x + b\/2a)\u00b2 \u2212 b\u00b2\/4a<\/div>\r\n  <\/div>\r\n\r\n  <div class=\"step final\">\r\n    <div class=\"step-title\">Step 4: Final Form<\/div>\r\n    <div class=\"formula\">y = a (x + b\/2a)\u00b2 \u2212 (b\u00b2 \u2212 4ac) \/ 4a<\/div>\r\n  <\/div>\r\n\r\n<\/div>\r\n\r\n<\/body>\r\n<\/html>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-5523e45 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5523e45\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-39bda88\" data-id=\"39bda88\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d773649 elementor-widget elementor-widget-text-editor\" data-id=\"d773649\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><strong>Comparing with the vertex form formula, we get:<\/strong><\/p><p><span style=\"font-weight: 400;\">h=-b\/2a,k=-(b\u00b2-4ac)\/4a<\/span><\/p><p><b>Final Vertex Formula(remember this, it&#8217;s very important)<\/b><\/p><p><span style=\"font-weight: 400;\">(h,k)=(-b\/2a,-(b\u00b2-4ac)\/4a<\/span><\/p><p><b>Quick Recap for the formulas<\/b><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The vertex formula helps find the turning point of a parabola<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The vertex of the parabola formula gives coordinates(h,k)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The vertex form formula is:<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0y=a(x-h)\u00b2+k<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><strong>You can use either:<\/strong><\/li><\/ul><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Direct formula<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u00a0Step-by-Step substitution<\/span><\/li><\/ol>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-2cf0ebb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2cf0ebb\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-8c62c33\" data-id=\"8c62c33\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fb29006 elementor-widget elementor-widget-html\" data-id=\"fb29006\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"max-width:700px;margin:auto;font-family:Arial;border:2px solid #4A90E2;border-radius:10px;overflow:hidden;background:#f0f8ff;\">\r\n\r\n  <div style=\"background:#4A90E2;color:#fff;padding:12px;font-size:18px;text-align:center;font-weight:bold;\">\r\n    Example 1: Vertex of a Parabola\r\n  <\/div>\r\n\r\n  <div style=\"padding:15px;\">\r\n\r\n    <table style=\"width:100%;border-collapse:collapse;font-size:14px;\">\r\n\r\n      <tr style=\"background:#e6f2ff;\">\r\n        <td style=\"padding:8px;font-weight:bold;\">Equation<\/td>\r\n        <td>y = 3x\u00b2 - 6x + 1<\/td>\r\n      <\/tr>\r\n\r\n      <tr>\r\n        <td style=\"padding:8px;font-weight:bold;\">Given<\/td>\r\n        <td>a = 3, b = -6, c = 1<\/td>\r\n      <\/tr>\r\n\r\n      <tr style=\"background:#e6f2ff;\">\r\n        <td style=\"padding:8px;font-weight:bold;\">Discriminant<\/td>\r\n        <td>D = b\u00b2 - 4ac = 36 - 12 = 24<\/td>\r\n      <\/tr>\r\n\r\n      <tr>\r\n        <td style=\"padding:8px;font-weight:bold;\">Vertex Formula<\/td>\r\n        <td>(h, k) = (-b\/2a, -D\/4a)<\/td>\r\n      <\/tr>\r\n\r\n      <tr style=\"background:#e6f2ff;\">\r\n        <td style=\"padding:8px;font-weight:bold;\">Calculation<\/td>\r\n        <td>(h, k) = (1, -2)<\/td>\r\n      <\/tr>\r\n\r\n      <tr>\r\n        <td style=\"padding:8px;font-weight:bold;\">Final Answer<\/td>\r\n        <td><b>Vertex = (1, -2)<\/b><\/td>\r\n      <\/tr>\r\n\r\n    <\/table>\r\n\r\n  <\/div>\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-a0570d6\" data-id=\"a0570d6\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-01ca711 elementor-widget elementor-widget-html\" data-id=\"01ca711\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"max-width:800px;margin:auto;font-family:Arial;background:#f4f8ff;border:2px solid #d6e4ff;border-radius:10px;overflow:hidden;box-shadow:0 4px 10px rgba(0,0,0,0.08);\">\r\n\r\n  <div style=\"background:#2b6cb0;color:#fff;padding:12px;text-align:center;font-size:18px;font-weight:bold;\">\r\n    Example 2: Vertex of a Parabola\r\n  <\/div>\r\n\r\n  <table style=\"width:100%;border-collapse:collapse;font-size:14px;\">\r\n    \r\n    <tr style=\"background:#eaf2ff;\">\r\n      <td style=\"padding:10px;font-weight:bold;width:25%;\">Given<\/td>\r\n      <td style=\"padding:10px;\">\r\n        x-intercepts: (2, 0), (3, 0)<br \/>\r\n        y-intercept: (0, 6)\r\n      <\/td>\r\n    <\/tr>\r\n\r\n    <tr>\r\n      <td style=\"padding:10px;font-weight:bold;\">Step 1<\/td>\r\n      <td style=\"padding:10px;\">\r\n        Form equation using intercepts:<br \/>\r\n        y = a(x - 2)(x - 3)\r\n      <\/td>\r\n    <\/tr>\r\n\r\n    <tr style=\"background:#eaf2ff;\">\r\n      <td style=\"padding:10px;font-weight:bold;\">Step 2<\/td>\r\n      <td style=\"padding:10px;\">\r\n        Substitute (0, 6):<br \/>\r\n        6 = a(0 - 2)(0 - 3) \u21d2 6 = 6a \u21d2 a = 1\r\n      <\/td>\r\n    <\/tr>\r\n\r\n    <tr>\r\n      <td style=\"padding:10px;font-weight:bold;\">Step 3<\/td>\r\n      <td style=\"padding:10px;\">\r\n        Equation becomes:<br \/>\r\n        y = (x - 2)(x - 3) = x\u00b2 - 5x + 6\r\n      <\/td>\r\n    <\/tr>\r\n\r\n    <tr style=\"background:#eaf2ff;\">\r\n      <td style=\"padding:10px;font-weight:bold;\">Step 4<\/td>\r\n      <td style=\"padding:10px;\">\r\n        Vertex formula:<br \/>\r\n        x = -b \/ 2a = 5\/2\r\n      <\/td>\r\n    <\/tr>\r\n\r\n    <tr>\r\n      <td style=\"padding:10px;font-weight:bold;\">Final Answer<\/td>\r\n      <td style=\"padding:10px;\">\r\n        Substitute x = 5\/2:<br \/>\r\n        y = -1\/4<br \/><br \/>\r\n        <b>Vertex = (5\/2, -1\/4)<\/b>\r\n      <\/td>\r\n    <\/tr>\r\n\r\n  <\/table>\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-4462fa6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4462fa6\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7fa887f\" data-id=\"7fa887f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4c6dd55 elementor-widget elementor-widget-html\" data-id=\"4c6dd55\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"max-width:700px;margin:20px auto;font-family:Arial;border-radius:10px;overflow:hidden;border:1px solid #ddd;\">\r\n\r\n  <!-- Header -->\r\n  <div style=\"background:#4A90E2;color:#fff;padding:12px;text-align:center;font-size:18px;font-weight:bold;\">\r\n    Example 3: Vertex of Parabola\r\n  <\/div>\r\n\r\n  <!-- Table -->\r\n  <table style=\"width:100%;border-collapse:collapse;font-size:14px;\">\r\n\r\n    <tr style=\"background:#f2f6ff;\">\r\n      <td style=\"padding:10px;font-weight:bold;width:30%;\">Given Equation<\/td>\r\n      <td style=\"padding:10px;\">y = 4x\u00b2 + 16x \u2212 16<\/td>\r\n    <\/tr>\r\n\r\n    <tr style=\"background:#ffffff;\">\r\n      <td style=\"padding:10px;font-weight:bold;\">Values<\/td>\r\n      <td style=\"padding:10px;\">a = 4, b = 16<\/td>\r\n    <\/tr>\r\n\r\n    <tr style=\"background:#f2f6ff;\">\r\n      <td style=\"padding:10px;font-weight:bold;\">Formula<\/td>\r\n      <td style=\"padding:10px;\">x = -b \/ 2a<\/td>\r\n    <\/tr>\r\n\r\n    <tr style=\"background:#ffffff;\">\r\n      <td style=\"padding:10px;font-weight:bold;\">Substitution<\/td>\r\n      <td style=\"padding:10px;\">x = -16 \/ (2 \u00d7 4) = -2<\/td>\r\n    <\/tr>\r\n\r\n    <tr style=\"background:#f2f6ff;\">\r\n      <td style=\"padding:10px;font-weight:bold;\">Find y<\/td>\r\n      <td style=\"padding:10px;\">y = 4(-2)\u00b2 + 16(-2) \u2212 16 = -32<\/td>\r\n    <\/tr>\r\n\r\n    <tr style=\"background:#dff5e1;\">\r\n      <td style=\"padding:10px;font-weight:bold;\">Final Answer<\/td>\r\n      <td style=\"padding:10px;font-weight:bold;\">Vertex = (-2, -32)<\/td>\r\n    <\/tr>\r\n\r\n  <\/table>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-6f5020d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6f5020d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7c34cf9\" data-id=\"7c34cf9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9bb2b8c elementor-widget elementor-widget-text-editor\" data-id=\"9bb2b8c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><strong><em>Read more related articles:<\/em><\/strong><\/p><p><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/how-to-find-the-area-of-a-circle\/\">\u2705How to Find the Area of a Circle?<\/a><\/p><p><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/horizontal-asymptote\/\">\u2705Horizontal Asymptote: Rules, Formula, and Easy Examples<\/a><\/p><p><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/how-to-find-the-radius-of-a-circle\/\">\u2705How to Find the Radius of a Circle: Easy Formulas and Examples<\/a><\/p><p><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/wallis-formula-integration-sine-cosine\/\">\u2705The Wallis Formula: Integrating Powers of Sine and Cosine Instantly<\/a><\/p><p class=\"elementor-post__title\"><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/kings-rule-in-definite-integrals\/\">\u2705How to Use King\u2019s Rule in Definite Integrals: Formulas &amp; Solved Examples<\/a><\/p><p class=\"elementor-post__title\"><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/use-of-cosine-formula\/\">\u2705How to Use the Cosine Formula to Find Missing Sides and Angles<\/a><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-138265f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"138265f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5085a8d\" data-id=\"5085a8d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a3425f9 elementor-widget elementor-widget-html\" data-id=\"a3425f9\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<!DOCTYPE html>\r\n<html lang=\"en\">\r\n<head>\r\n<meta charset=\"UTF-8\"\/>\r\n<title>Vertex Formula Title<\/title>\r\n\r\n<style>\r\n  body {\r\n    margin: 0;\r\n    padding: 0;\r\n    font-family: Arial, sans-serif;\r\n    background: #f4f4f4;\r\n  }\r\n\r\n  .title-container {\r\n    display: flex;\r\n    justify-content: center;\r\n    align-items: center;\r\n    padding: 0px 10px;\r\n  }\r\n\r\n  .title-box {\r\n    position: relative;\r\n    background: linear-gradient(135deg, #7c3aed, #2563eb);\r\n    padding: 20px 40px;\r\n    border-radius: 50px;\r\n    color: #fff;\r\n    text-align: center;\r\n    box-shadow: 0 10px 25px rgba(0,0,0,0.2);\r\n  }\r\n\r\n  \/* Decorative shapes *\/\r\n  .title-box::before,\r\n  .title-box::after {\r\n    content: \"\";\r\n    position: absolute;\r\n    width: px;\r\n    height: px;\r\n    background: #10b981;\r\n    border-radius: 50%;\r\n    top: 50%;\r\n    transform: translateY(-50%);\r\n  }\r\n\r\n  .title-box::before {\r\n    left: -15px;\r\n  }\r\n\r\n  .title-box::after {\r\n    right: -15px;\r\n  }\r\n\r\n  .title-box h1 {\r\n    margin: 0;\r\n    font-size: 34px;\r\n    letter-spacing: 1px;\r\n  }\r\n<\/style>\r\n\r\n<\/head>\r\n<body>\r\n\r\n<div class=\"title-container\">\r\n  <div class=\"title-box\">\r\n    <h6>Conclusion\r\n\r\n  <\/h6><\/div>\r\n<\/div>\r\n\r\n<\/body>\r\n<\/html>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-f18072a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f18072a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f39039b\" data-id=\"f39039b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cb4009b elementor-widget elementor-widget-text-editor\" data-id=\"cb4009b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">This formula is your ultimate shortcut to finding the turning point of a parabola without any confusion. Whether you&#8217;re using the vertex of a parabola formula directly or converting into the vertex form formula, both methods lead you to the same goal\u2014the exact coordinates of the vertex (h,k).<\/span><\/p><h5><strong>By now, you&#8217;ve learned:<\/strong><\/h5><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">What is the vertex formula, and why does it matter<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">How the standard form y-ax\u00b2+bx+c connects to the vertex<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Two easy ways to apply the vertex of a parabola formula<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Step-by-step examples to build confidence<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">The best part is that once you understand this concept, solving quadratic equations becomes faster, easier, and even fun. So next time you see a parabola, remember\u2014The vertex is the star of the graph, and the vertex formula is your tool to find it instantly.<\/span><\/p><p><span style=\"font-weight: 400;\">You can opt for our <\/span><a href=\"https:\/\/moonpreneur.com\/innovator-program\/advanced-math\/\"><span style=\"font-weight: 400;\">Advanced Math<\/span><\/a><span style=\"font-weight: 400;\"> or Vedic Math+Mental Math courses. Our <\/span><a href=\"https:\/\/mp.moonpreneur.com\/math-quiz-for-kids\/\"><span style=\"font-weight: 400;\">Math Quiz<\/span><\/a><span style=\"font-weight: 400;\"> for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.\u00a0<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-55dc29d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"55dc29d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-99d5f3b\" data-id=\"99d5f3b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-55b312e elementor-widget elementor-widget-text-editor\" data-id=\"55b312e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h4><strong>FAQS<\/strong><\/h4>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-945d4ec elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"945d4ec\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2c312b4\" data-id=\"2c312b4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-595dd56 elementor-widget elementor-widget-toggle\" data-id=\"595dd56\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9371\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-9371\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">1. How to remember vertex formula?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-9371\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-9371\"><p><b>Ans. f (x) = a(x &#8211; h)<sup>2<\/sup>\u00a0+ k<\/b>, where (h, k) is the vertex of the parabola. Remember: the &#8220;vertex? is the &#8220;turning point&#8221;. When written in &#8220;vertex form&#8221;: (h, k) is the vertex of the parabola, and x = h is the axis of symmetry.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9372\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-9372\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">2. Is there a vertex formula?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-9372\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-9372\"><p><span style=\"font-weight: 400;\"><strong>Ans.<\/strong> <b>The vertex formula helps to find the vertex coordinates of a parabola<\/b>. The standard form of a parabola is y = ax<sup>2<\/sup>\u00a0+ bx + c. The vertex form of the parabola y = a(x &#8211; h)<sup>2<\/sup>\u00a0+ k. There are two ways in which we can determine the vertex(h, k).<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9373\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-9373\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">3. What is the vertex of \u2220 ABC?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-9373\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-9373\"><p><span style=\"font-weight: 400;\"><strong>Ans.<\/strong> By convention, when naming an angle with three letters, the vertex is always the middle letter. It represents the exact point or corner where the two rays <em>(arms BA<\/em><\/span><em> and BC)<\/em> meet to form the angle.<\/p><p><span style=\"font-weight: 400;\">\u00a0<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9374\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-9374\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\"> 4. What is vertex in math?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-9374\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-9374\"><p><span style=\"font-weight: 400;\"><strong>Ans. <\/strong>In mathematics, a\u00a0<strong class=\"Yjhzub\" data-sfc-root=\"c\" data-sfc-cb=\"\">vertex<\/strong>\u00a0(plural:\u00a0<strong class=\"Yjhzub\" data-sfc-root=\"c\" data-sfc-cb=\"\">vertices<\/strong>) is\u00a0<mark class=\"HxTRcb\" data-sfc-root=\"c\" data-wiz-uids=\"yzYn2_e\" data-sfc-cb=\"\" data-ved=\"2ahUKEwjRnMvlp9mUAxULwzgGHexYK6AQuJAPeggIAAgBCAEQBQ\">a specific point where two or more line segments, lines, or edges meet<\/mark>. It essentially refers to a corner or an intersection point.<span class=\"WBgIic notranslate\" data-sfc-root=\"c\" data-wiz-uids=\"yzYn2_g,yzYn2_h\" data-sfc-cb=\"\"><span class=\"NMq1me\" data-animation-atomic=\"\" data-wiz-attrbind=\"class=yzYn2_f\/TKHnVd\"><span aria-hidden=\"true\">\u00a0<\/span><\/span><\/span><\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9375\" class=\"elementor-tab-title\" data-tab=\"5\" role=\"button\" aria-controls=\"elementor-tab-content-9375\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">5. How to find vertex location?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-9375\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"5\" role=\"region\" aria-labelledby=\"elementor-tab-title-9375\"><p><strong>Ans.<\/strong> You can use this handy formula: <b>x = -b \/ 2a<\/b>. Once you have the x-coordinate, you can plug it back into the original quadratic equation to find the corresponding y-coordinate. So, y = a(-b\/2a)\u00b2 + b(-b\/2a) + c. This gives you the full coordinates of the vertex (x, y).<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9376\" class=\"elementor-tab-title\" data-tab=\"6\" role=\"button\" aria-controls=\"elementor-tab-content-9376\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">6. What is 2\u03c0 equal to? <\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-9376\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"6\" role=\"region\" aria-labelledby=\"elementor-tab-title-9376\"><p>Ans.<\/p><p><span style=\"font-weight: 400;\">Ans. Approximately <\/span><span style=\"font-weight: 400;\">2\u03c0 is equal to <\/span><span style=\"font-weight: 400;\">6.28<\/span><\/p><p><span style=\"font-weight: 400;\">2\u03c0 means 2\u00d7 \u03c0 (pi)<\/span><\/p><p><span style=\"font-weight: 400;\">Since \u00d7 \u03c0 \u2248 3.14:<\/span><\/p><p><span style=\"font-weight: 400;\">2\u03c0 =2\u00d73.14 =6.28<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9377\" class=\"elementor-tab-title\" data-tab=\"7\" role=\"button\" aria-controls=\"elementor-tab-content-9377\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">7. What are the 7 parts of a circle? <\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-9377\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"7\" role=\"region\" aria-labelledby=\"elementor-tab-title-9377\"><p><span style=\"font-weight: 400;\">Ans. The most common and basic parts of a circle are the Center, Radius, diameter, circumference, chord, Arc and Tangent.\u00a0<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-9378\" class=\"elementor-tab-title\" data-tab=\"8\" role=\"button\" aria-controls=\"elementor-tab-content-9378\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">8. What is a semicircle? <\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-9378\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"8\" role=\"region\" aria-labelledby=\"elementor-tab-title-9378\"><p><span style=\"font-weight: 400;\">Ans. A semicircle is half a circle. When you divide a circle into two equal parts along its diameter, the two parts are called semicircles.<\/span><\/p><p><span style=\"font-weight: 400;\">Key features:<\/span><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It is made by cutting a circle through its diameter<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It has:<\/span><\/li><\/ol><p><span style=\"font-weight: 400;\">-One curved side (half of a circle)<\/span><\/p><p><span style=\"font-weight: 400;\">-One line straight (the diameter). Simple example:<\/span><\/p><p><span style=\"font-weight: 400;\">Imagine:<\/span><\/p><p><span style=\"font-weight: 400;\">\ud83c\udf55 Pizza (half)\u00a0 and\ud83c\udf19 Moon (half) are real instances of a semicircle!<\/span><\/p><p><span style=\"font-weight: 400;\">Important Formulas<\/span><\/p><p><span style=\"font-weight: 400;\">Area of a semicircle = half of the area of a circle. Area = 21\u200b\u03c0r2\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">A semicircle is just half of a circle, but it still has all the same rules and formulas; just remember to divide by 2!\u00a0<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The Vertex Formula? Adjust b value: b = 6 x = -1.5 Formula x = -b \/ 2a a (constant) 2 b value 6 Vertex (x) -1.5 Imagine you&#8217;re on a roller coaster. You go up&#8230; up&#8230; up and suddenly &#8211; whoosh\u2014whoosh!\u2014you reach the highest point and start coming down. Or maybe you&#8217;re in a [&hellip;]<\/p>\n","protected":false},"author":116,"featured_media":38588,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[979],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/38507"}],"collection":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/comments?post=38507"}],"version-history":[{"count":37,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/38507\/revisions"}],"predecessor-version":[{"id":38600,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/38507\/revisions\/38600"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media\/38588"}],"wp:attachment":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media?parent=38507"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/categories?post=38507"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/tags?post=38507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}