{"id":181403,"date":"2025-01-10T17:49:36","date_gmt":"2025-01-10T17:49:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=181403"},"modified":"2025-01-10T17:49:39","modified_gmt":"2025-01-10T17:49:39","slug":"unit-3-parent-functions-transformations-name","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/10\/unit-3-parent-functions-transformations-name\/","title":{"rendered":"Unit 3: Parent Functions &amp; Transformations Name"},"content":{"rendered":"\n<p>Unit 3: Parent Functions &amp; Transformations Name: Bell: Homework 5: Vertex Form of a Quadratic Equation Date: ** This is a 2-page documenti Describe the transformation of each function compared to its parent function. 1. f(x) &#8211; (x-4 .9 Horizontal shift to the right vertical stretch by a tactor of 2 04 A nits &#8220;Reflection aloout the ans. vertical shift up by 9 units Vertical shift dam by 3 units Horizontal Shil 3. f(x) = (x+6) to the left by 4. (x)=-7-7- 1 38 SO T Gunit Reflection about the starit, Vertical compression by a factor vertical shift down by lunft Petro 3 Vertical stretch by 6. f(x) = &#8211; 2 (x &#8211; 5)\u00b2 + 2 Hoe right by &amp; fach Reflection about the x-axist Vertical shift up by 2 units Give the vertex and axis of symmetry of each equation\/inequality, then graph. 7. \/(x) = (x+1)-8 8. S(x) = (x+5)* +5 3. S (x) &#8211; 2 factor of 3\/27 9.50)=2x-3 10. f()=-3(x-4) +1 -2 lfx=4 +8f1 12.\/8)= 10-4) -5&#215;24 11. 5 &#8211; 2x 1fx>1 13. f(x) > 14. f(x)2 47\u00b0 -7 15. f(x)<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>It seems like you&#8217;re working on a math worksheet related to quadratic functions in vertex form and their transformations. Here&#8217;s a structured explanation of how to approach this type of problem, including a detailed breakdown of transformations, vertex, and axis of symmetry:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Understanding the Vertex Form:<\/h3>\n\n\n\n<p>The vertex form of a quadratic equation is:<br>f(x)=a(x\u2212h)2+kf(x) = a(x-h)^2 + k<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>hh: Horizontal shift (right if h>0h > 0, left if h&lt;0h &lt; 0).<\/li>\n\n\n\n<li>kk: Vertical shift (up if k>0k > 0, down if k&lt;0k &lt; 0).<\/li>\n\n\n\n<li>aa: Controls the vertical stretch\/compression and reflection.\n<ul class=\"wp-block-list\">\n<li>If \u2223a\u2223>1|a| > 1: Vertical stretch.<\/li>\n\n\n\n<li>If 0&lt;\u2223a\u2223&lt;10 &lt; |a| &lt; 1: Vertical compression.<\/li>\n\n\n\n<li>If a&lt;0a &lt; 0: Reflection about the x-axis.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Steps for Each Problem:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify the Transformations<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Compare the given equation with the parent function f(x)=x2f(x) = x^2.<\/li>\n\n\n\n<li>Note any horizontal shifts (hh), vertical shifts (kk), and changes to the coefficient (aa).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Find the Vertex<\/strong>:\n<ul class=\"wp-block-list\">\n<li>The vertex is (h,k)(h, k).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Determine the Axis of Symmetry<\/strong>:\n<ul class=\"wp-block-list\">\n<li>The axis of symmetry is the vertical line x=hx = h.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Graph the Function<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Plot the vertex.<\/li>\n\n\n\n<li>Use the direction of opening (upward if a>0a > 0, downward if a&lt;0a &lt; 0) and the stretch\/compression factor to sketch the parabola.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Example Breakdown:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Problem 1: f(x)=2(x\u22124)2+9f(x) = 2(x &#8211; 4)^2 + 9<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Transformations<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Horizontal shift: Right by 4 units.<\/li>\n\n\n\n<li>Vertical stretch: By a factor of 2.<\/li>\n\n\n\n<li>Vertical shift: Up by 9 units.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Vertex<\/strong>: (4,9)(4, 9).<\/li>\n\n\n\n<li><strong>Axis of Symmetry<\/strong>: x=4x = 4.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Problem 2: f(x)=\u221213(x+6)2\u22121f(x) = -\\frac{1}{3}(x+6)^2 &#8211; 1<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Transformations<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Horizontal shift: Left by 6 units.<\/li>\n\n\n\n<li>Vertical compression: By a factor of 13\\frac{1}{3}.<\/li>\n\n\n\n<li>Reflection: About the x-axis (due to the negative aa).<\/li>\n\n\n\n<li>Vertical shift: Down by 1 unit.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Vertex<\/strong>: (\u22126,\u22121)(-6, -1).<\/li>\n\n\n\n<li><strong>Axis of Symmetry<\/strong>: x=\u22126x = -6.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">For the Writing Portion:<\/h3>\n\n\n\n<p>In a 300-word explanation, you would:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Describe the significance of the vertex form.<\/li>\n\n\n\n<li>Explain how each parameter (aa, hh, kk) affects the graph.<\/li>\n\n\n\n<li>Highlight the step-by-step process for analyzing transformations, finding the vertex, and determining the axis of symmetry.<\/li>\n\n\n\n<li>Discuss how changes in aa influence the parabola&#8217;s shape and orientation.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Would you like further assistance with specific problems or the 300-word explanation?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Unit 3: Parent Functions &amp; Transformations Name: Bell: Homework 5: Vertex Form of a Quadratic Equation Date: ** This is a 2-page documenti Describe the transformation of each function compared to its parent function. 1. f(x) &#8211; (x-4 .9 Horizontal shift to the right vertical stretch by a tactor of 2 04 A nits &#8220;Reflection [&hellip;]<\/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-181403","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181403","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=181403"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181403\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=181403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=181403"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=181403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}