{"id":162391,"date":"2024-11-06T17:44:26","date_gmt":"2024-11-06T17:44:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=162391"},"modified":"2024-11-06T17:44:29","modified_gmt":"2024-11-06T17:44:29","slug":"list-the-key-features-of-the-quadratic-function-graphed","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/06\/list-the-key-features-of-the-quadratic-function-graphed\/","title":{"rendered":"L\u00edst the key features of the quadratic function graphed"},"content":{"rendered":"\n

L\u00edst the key features of the quadratic function graphed.
A) x-intercepts: (0,0), y-intercept: (0,10), vertex (3,-1)
B) x-intercepts: none, y-intercept: (0,-10), vertex: (3,-1)
C) x-intercepts: (0.-10), y-intercept: none, vertex: (3,-1)
D) x-intercepts: none, y’intercept: (3,-1), vertex (0-10)<\/p>\n\n\n\n

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

The correct answer is B) x-intercepts: none, y-intercept: (0, -10), vertex: (3, -1)<\/strong>.<\/p>\n\n\n\n

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

A quadratic function<\/strong> is typically in the form (y = ax^2 + bx + c), and its graph is a parabola<\/strong>. Key features of a quadratic function include the x-intercepts<\/strong>, y-intercept<\/strong>, and vertex<\/strong>.<\/p>\n\n\n\n

    \n
  1. x-intercepts<\/strong>: These are the points where the graph crosses the x-axis (where (y = 0)). If there are no x-intercepts, the parabola does not touch or cross the x-axis, indicating that the quadratic equation does not have real solutions. In this case, the graph has no x-intercepts<\/strong> (as specified in option B).<\/li>\n\n\n\n
  2. y-intercept<\/strong>: This is the point where the graph crosses the y-axis (where (x = 0)). The y-intercept is found by plugging (x = 0) into the quadratic equation and solving for (y). In option B, the y-intercept is ((0, -10)), meaning that when (x = 0), the value of (y) is (-10).<\/li>\n\n\n\n
  3. Vertex<\/strong>: The vertex is the highest or lowest point on the graph, depending on the direction the parabola opens (upwards for a positive (a), downwards for a negative (a)). The vertex in option B is ((3, -1)), meaning the point ((3, -1)) is the turning point of the parabola, which opens upwards because the vertex represents the minimum point.<\/li>\n<\/ol>\n\n\n\n

    Why Option B is Correct:<\/h3>\n\n\n\n
      \n
    • The x-intercepts<\/strong> in option B are listed as “none,” which means the parabola does not cross the x-axis. This suggests the equation has no real solutions or the graph does not intersect the x-axis.<\/li>\n\n\n\n
    • The y-intercept<\/strong> is ((0, -10)), which matches the description in option B. This is where the graph intersects the y-axis, and it is consistent with the given data.<\/li>\n\n\n\n
    • The vertex<\/strong> at ((3, -1)) represents the lowest point of the parabola, confirming that the graph opens upward.<\/li>\n<\/ul>\n\n\n\n

      Why Other Options are Incorrect:<\/h3>\n\n\n\n
        \n
      • Option A<\/strong> has an incorrect y-intercept and vertex. The y-intercept is ((0, 10)), but it should be ((0, -10)), and the x-intercepts are also wrongly listed.<\/li>\n\n\n\n
      • Option C<\/strong> suggests the x-intercepts are ((0, -10)), but that is incorrect because (x)-intercepts should not have a y-value of -10. Additionally, there is no y-intercept in this option.<\/li>\n\n\n\n
      • Option D<\/strong> lists the vertex as ((3, -1)), but the y-intercept is incorrectly shown as ((3, -10)), and this is inconsistent with the vertex and overall graph characteristics.<\/li>\n<\/ul>\n\n\n\n

        Thus, option B is the best description of the given quadratic function.<\/p>\n","protected":false},"excerpt":{"rendered":"

        L\u00edst the key features of the quadratic function graphed.A) x-intercepts: (0,0), y-intercept: (0,10), vertex (3,-1)B) x-intercepts: none, y-intercept: (0,-10), vertex: (3,-1)C) x-intercepts: (0.-10), y-intercept: none, vertex: (3,-1)D) x-intercepts: none, y’intercept: (3,-1), vertex (0-10) The Correct Answer and Explanation is : The correct answer is B) x-intercepts: none, y-intercept: (0, -10), vertex: (3, -1). Explanation: A […]<\/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-162391","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162391","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=162391"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162391\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=162391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=162391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=162391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}