{"id":249244,"date":"2025-07-09T05:21:07","date_gmt":"2025-07-09T05:21:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249244"},"modified":"2025-07-09T05:21:09","modified_gmt":"2025-07-09T05:21:09","slug":"vertex-form-of-a-quadratic-equation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/vertex-form-of-a-quadratic-equation\/","title":{"rendered":"Vertex Form of a Quadratic Equation *"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Here are the correct descriptions of the transformations for each function, followed by a detailed explanation.<\/p>\n\n\n\n

Correct Answers<\/h3>\n\n\n\n
    \n
  1. f(x) = (x – 4)\u00b2 + 9:<\/strong>\u00a0The parent function is translated 4 units to the right and 9 units up.<\/li>\n\n\n\n
  2. f(x) = -2x\u00b2 – 3:<\/strong>\u00a0The parent function is reflected across the x-axis, vertically stretched by a factor of 2, and translated 3 units down.<\/li>\n\n\n\n
  3. f(x) = \u00bc(x + 6)\u00b2:<\/strong>\u00a0The parent function is vertically compressed by a factor of 1\/4 and translated 6 units to the left.<\/li>\n\n\n\n
  4. f(x) = -(x – 7)\u00b2 – 1:<\/strong>\u00a0The parent function is reflected across the x-axis, translated 7 units to the right, and 1 unit down.<\/li>\n\n\n\n
  5. f(x) = (3\/2)x\u00b2:<\/strong>\u00a0The parent function is vertically stretched by a factor of 3\/2.<\/li>\n\n\n\n
  6. f(x) = -\u2154(x – 5)\u00b2 + 2:<\/strong>\u00a0The parent function is reflected across the x-axis, vertically compressed by a factor of 2\/3, translated 5 units to the right, and 2 units up.<\/li>\n<\/ol>\n\n\n\n

    Explanation<\/h3>\n\n\n\n

    Understanding the transformations of a quadratic function involves comparing it to its parent function, f(x) = x\u00b2. The vertex form, f(x) = a(x – h)\u00b2 + k, provides a clear guide to these changes. Each parameter, a, h, and k, corresponds to a specific transformation that alters the shape, orientation, or position of the parent parabola.<\/p>\n\n\n\n

    The parameter a determines the parabola’s vertical scale and orientation. If a is negative, the parabola reflects across the x-axis and opens downward. If the absolute value of a is greater than 1, the graph is vertically stretched, making it appear narrower than the parent function. If the absolute value of a is between 0 and 1, the graph is vertically compressed, or shrunk, which makes it appear wider.<\/p>\n\n\n\n

    The parameter h dictates the horizontal shift, or translation, of the parabola. The graph moves h units to the right for a term like (x – h). Conversely, it moves h units to the left for a term like (x + h), because this can be rewritten as (x – (-h)).<\/p>\n\n\n\n

    Finally, the parameter k controls the vertical shift. A positive value for k moves the graph upward by k units, while a negative value for k moves it downward by k units. The combination of these shifts moves the vertex of the parabola from the origin (0,0) of the parent function to a new location at the point (h, k). By analyzing these three parameters for each equation, we can fully describe its transformation from the original f(x) = x\u00b2.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    The Correct Answer and Explanation is: Here are the correct descriptions of the transformations for each function, followed by a detailed explanation. Correct Answers Explanation Understanding the transformations of a quadratic function involves comparing it to its parent function, f(x) = x\u00b2. The vertex form, f(x) = a(x – h)\u00b2 + k, provides a clear guide to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-249244","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249244","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=249244"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249244\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}