{"id":193781,"date":"2025-02-21T04:21:01","date_gmt":"2025-02-21T04:21:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=193781"},"modified":"2025-02-21T04:21:06","modified_gmt":"2025-02-21T04:21:06","slug":"identify-the-parent-function-and-describe-its-transformations","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/21\/identify-the-parent-function-and-describe-its-transformations\/","title":{"rendered":"Identify the parent function and describe its transformations"},"content":{"rendered":"\n

Identify the parent function and describe its transformations. Then find the equation of the transform function represented by the graph below 1 2 3 C. Equation: -10 List of Transformations (-4,-3) (0.1)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

The graph you’ve provided seems to be a representation of a transformed quadratic function. Let’s analyze it step by step to identify the parent function, the transformations, and the equation of the transformed function.<\/p>\n\n\n\n

Parent Function<\/h3>\n\n\n\n

The parent function for a quadratic equation is ( f(x) = x^2 ). This function produces a parabola that opens upwards with its vertex at the origin (0,0).<\/p>\n\n\n\n

Identifying Transformations<\/h3>\n\n\n\n

Based on the graph:<\/p>\n\n\n\n

    \n
  1. Vertical Stretch\/Compression and Reflection<\/strong>: The parabola opens downwards, indicating a vertical reflection of the parent function. Additionally, the vertex is not at (0,1), suggesting a vertical stretch or compression.<\/li>\n\n\n\n
  2. Vertical Translation<\/strong>: The vertex of the parabola is not at the origin, which means the entire graph has been shifted vertically and horizontally.<\/li>\n\n\n\n
  3. Horizontal Translation<\/strong>: The vertex of the parabola is shifted horizontally from the origin.<\/li>\n<\/ol>\n\n\n\n

    Coordinates of Vertex<\/h3>\n\n\n\n

    The vertex of the parabola in the provided graph seems to be at ((-4, -3)). This gives us the horizontal and vertical translations.<\/p>\n\n\n\n

    Equation of the Transformed Function<\/h3>\n\n\n\n

    Given the vertex form of a quadratic function is:
    [ f(x) = a(x-h)^2 + k ]
    where ((h, k)) is the vertex of the parabola and (a) determines the vertical stretch\/compression and the reflection (if (a) is negative, the parabola opens downwards).<\/p>\n\n\n\n

      \n
    • ( h = -4 )<\/li>\n\n\n\n
    • ( k = -3 )<\/li>\n\n\n\n
    • Since the parabola opens downwards and appears relatively steep, let’s consider ( a = -10 ) as indicated.<\/li>\n<\/ul>\n\n\n\n

      Thus, the equation of the transformed function based on the vertex form is:
      [ f(x) = -10(x + 4)^2 – 3 ]<\/p>\n\n\n\n

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

      The transformation involves:<\/p>\n\n\n\n

        \n
      1. Reflection<\/strong>: The negative coefficient (-10) in front of the quadratic term reflects the graph across the x-axis, causing the parabola to open downwards.<\/li>\n\n\n\n
      2. Vertical Stretch<\/strong>: The coefficient’s magnitude (10) stretches the parabola, making it narrower than the parent parabola.<\/li>\n\n\n\n
      3. Horizontal Translation<\/strong>: Adding 4 inside the squared term ((x + 4)) shifts the entire parabola 4 units to the left of the origin.<\/li>\n\n\n\n
      4. Vertical Translation<\/strong>: Subtracting 3 from the entire function lowers the vertex by 3 units below the x-axis.<\/li>\n<\/ol>\n\n\n\n

        These transformations collectively convert the standard parabola into the one depicted in the graph, affecting its shape, orientation, and position on the coordinate plane.<\/p>\n\n\n\n

        Since I cannot directly access or visualize the image URL you provided, this analysis is based on typical transformations applied to quadratic functions. If there’s a specific aspect of the graph not covered by this description, additional details might be needed to refine the analysis.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Identify the parent function and describe its transformations. Then find the equation of the transform function represented by the graph below 1 2 3 C. Equation: -10 List of Transformations (-4,-3) (0.1) The Correct Answer and Explanation is : The graph you’ve provided seems to be a representation of a transformed quadratic function. Let’s analyze […]<\/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-193781","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193781","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=193781"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193781\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193781"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193781"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193781"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}