{"id":244507,"date":"2025-07-05T07:49:39","date_gmt":"2025-07-05T07:49:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=244507"},"modified":"2025-07-05T07:49:41","modified_gmt":"2025-07-05T07:49:41","slug":"use-the-graphing-calculator-to-graph-the-quadratic-function-y2x2%e2%88%926x%e2%88%928","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/05\/use-the-graphing-calculator-to-graph-the-quadratic-function-y2x2%e2%88%926x%e2%88%928\/","title":{"rendered":"Use the graphing calculator to graph the quadratic function\u00a0y=2×2\u22126x\u22128."},"content":{"rendered":"\n
Use the graphing calculator to graph the quadratic function y=2x2\u22126x\u22128.<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
The correct options are -1<\/strong> and 4<\/strong>.<\/p>\n\n\n\n
Explanation:<\/strong><\/p>\n\n\n\n
The problem asks for the solutions to the quadratic equation 0 = 2x\u00b2 – 6x – 8. Finding the solutions, or roots, of this equation is equivalent to finding the x-intercepts of the related quadratic function y = 2x\u00b2 – 6x – 8. The x-intercepts are the points on the graph where the function crosses the x-axis, which occurs when the y-value is zero.<\/p>\n\n\n\n
The prompt suggests using a graphing calculator. If you were to graph the function y = 2x\u00b2 – 6x – 8, you would see a parabola that opens upwards. The points where this parabola intersects the horizontal x-axis are the solutions. The graph would cross the x-axis at x = -1 and x = 4. Therefore, these are the two solutions to the equation.<\/p>\n\n\n\n
Even without a graphing calculator, we can verify the solutions algebraically. The most direct method for a multiple-choice question is to substitute the given options into the equation and see which ones make the statement true.<\/p>\n\n\n\n
Let’s test the correct options:<\/p>\n\n\n\n
    \n
  1. Test x = -1:<\/strong>\n
      \n
    • 2(-1)\u00b2 – 6(-1) – 8<\/li>\n\n\n\n
    • 2(1) – (-6) – 8<\/li>\n\n\n\n
    • 2 + 6 – 8<\/li>\n\n\n\n
    • 8 – 8 = 0
      Since\u00a00 = 0, the equation holds true. Thus,\u00a0-1<\/strong>\u00a0is a solution.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Test x = 4:<\/strong>\n
        \n
      • 2(4)\u00b2 – 6(4) – 8<\/li>\n\n\n\n
      • 2(16) – 24 – 8<\/li>\n\n\n\n
      • 32 – 24 – 8<\/li>\n\n\n\n
      • 8 – 8 = 0
        Since\u00a00 = 0, the equation also holds true. Thus,\u00a04<\/strong>\u00a0is a solution.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
        Another algebraic method is factoring. First, we can simplify the equation by dividing all terms by their greatest common factor, which is 2:
        (2x\u00b2 – 6x – 8) \/ 2 = 0 \/ 2
        x\u00b2 – 3x – 4 = 0<\/p>\n\n\n\n
        Next, we look for two numbers that multiply to -4 and add to -3. These numbers are -4 and 1. We can then write the equation in factored form:
        (x – 4)(x + 1) = 0<\/p>\n\n\n\n
        According to the zero product property, if the product of two factors is zero, at least one of the factors must be zero.<\/p>\n\n\n\n
          \n
        • x – 4 = 0\u00a0\u2192\u00a0x = 4<\/li>\n\n\n\n
        • x + 1 = 0\u00a0\u2192\u00a0x = -1<\/li>\n<\/ul>\n\n\n\n
          Both algebraic methods confirm that the two solutions are -1 and 4<\/p>\n\n\n\n
          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
          Use the graphing calculator to graph the quadratic function y=2×2\u22126x\u22128. The Correct Answer and Explanation is: The correct options are -1 and 4. Explanation: The problem asks for the solutions to the quadratic equation 0 = 2x\u00b2 – 6x – 8. Finding the solutions, or roots, of this equation is equivalent to finding the x-intercepts of the related quadratic function y […]<\/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-244507","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244507","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=244507"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244507\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=244507"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=244507"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=244507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}