{"id":145998,"date":"2024-09-30T06:24:11","date_gmt":"2024-09-30T06:24:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=145998"},"modified":"2024-09-30T06:24:13","modified_gmt":"2024-09-30T06:24:13","slug":"find-the-axis-of-symmetry-for-the-parabola-whose-equation-is-given","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/30\/find-the-axis-of-symmetry-for-the-parabola-whose-equation-is-given\/","title":{"rendered":"Find the axis of symmetry for the parabola whose equation is given"},"content":{"rendered":"\n<p>Find the axis of symmetry for the parabola whose equation is given. Use the axis of symmetry to find a second point on the parabola whose y-coordinate is tho same. as the given point. f(x)=2(x+3)<br>2<br>\u22121:(\u22122,1) The axis of symmetry is (Type an equation Simply your answer)<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To find the axis of symmetry for the parabola given by the equation ( f(x) = 2(x + 3)^2 &#8211; 1 ), we can use the general form of a quadratic function, which is ( f(x) = a(x &#8211; h)^2 + k ). In this form, ((h, k)) is the vertex of the parabola, and the axis of symmetry can be represented by the vertical line ( x = h ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the Vertex<\/h3>\n\n\n\n<p>The equation ( f(x) = 2(x + 3)^2 &#8211; 1 ) can be rewritten to identify ( h ) and ( k ):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Here, ( a = 2 ), ( h = -3 ), and ( k = -1 ).<\/li>\n\n\n\n<li>Thus, the vertex of the parabola is at the point ((-3, -1)).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Determine the Axis of Symmetry<\/h3>\n\n\n\n<p>The axis of symmetry for this parabola is the vertical line that passes through the vertex, given by the equation:<\/p>\n\n\n\n<p>[<br>x = -3<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find a Second Point<\/h3>\n\n\n\n<p>To find a second point on the parabola that has the same ( y )-coordinate as the given point ((-2, 1)), we first evaluate ( f(x) ) to find where ( f(x) = 1 ):<\/p>\n\n\n\n<p>[<br>1 = 2(x + 3)^2 &#8211; 1<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Solve for ( x )<\/h3>\n\n\n\n<p>Rearranging the equation:<\/p>\n\n\n\n<p>[<br>2(x + 3)^2 = 2 \\implies (x + 3)^2 = 1<br>]<\/p>\n\n\n\n<p>Taking the square root of both sides gives:<\/p>\n\n\n\n<p>[<br>x + 3 = \\pm 1<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Find the Possible Values for ( x )<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>For ( x + 3 = 1 ):<br>[<br>x = 1 &#8211; 3 = -2<br>]<\/li>\n\n\n\n<li>For ( x + 3 = -1 ):<br>[<br>x = -1 &#8211; 3 = -4<br>]<\/li>\n<\/ol>\n\n\n\n<p>Thus, the two ( x )-values where the ( y )-coordinate is the same (1) are ( x = -2 ) and ( x = -4 ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Therefore, the axis of symmetry is ( x = -3 ), and the second point on the parabola with the same ( y )-coordinate as ((-2, 1)) is ((-4, 1)). This shows the symmetry of the parabola around its axis, as the ( x )-values of the points are equidistant from the axis of symmetry.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the axis of symmetry for the parabola whose equation is given. Use the axis of symmetry to find a second point on the parabola whose y-coordinate is tho same. as the given point. f(x)=2(x+3)2\u22121:(\u22122,1) The axis of symmetry is (Type an equation Simply your answer) The Correct Answer and Explanation is : To find [&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-145998","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145998","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=145998"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/145998\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=145998"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=145998"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=145998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}