{"id":257464,"date":"2025-07-17T12:33:48","date_gmt":"2025-07-17T12:33:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=257464"},"modified":"2025-07-17T12:33:50","modified_gmt":"2025-07-17T12:33:50","slug":"determine-the-value-of-the-zeros-the-equation-of-the-axis-of-symmetry-the-max-or-min-value-and-the-vertex","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/17\/determine-the-value-of-the-zeros-the-equation-of-the-axis-of-symmetry-the-max-or-min-value-and-the-vertex\/","title":{"rendered":"Determine the value of the zeros, the equation of the axis of symmetry, the max or min value and the vertex"},"content":{"rendered":"\n

Find zeros, max and min classroom.google.com Algebra 1 8.2 Worksheet Characteristics of Quadratic Functions Name Per____Date____ Determine the value of the zeros, the equation of the axis of symmetry, the max or min value and the vertex. 1. 2. 3. Zeros: Axis of symmetry: Max or Min: Vertex: 4 Zeros: Axis of symmetry: Max or Min: Vertex: 5. Zeros: Axis of symmetry: Max or Min: Vertex: 6. Page 1\/2 Q<\/p>\n\n\n\n

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

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

Let’s analyze each of the three graphs (problems 1 to 3) from the worksheet titled “Characteristics of Quadratic Functions”<\/strong>. For each graph, we will identify the zeros<\/strong>, axis of symmetry<\/strong>, maximum or minimum<\/strong>, and vertex<\/strong> based on the visual data.<\/p>\n\n\n\n

\n\n\n\n

Problem 1<\/strong>:<\/h3>\n\n\n\n
    \n
  • Zeros<\/strong>: The parabola crosses the x-axis at x = -3<\/strong> and x = 1<\/strong>.<\/li>\n\n\n\n
  • Axis of Symmetry<\/strong>: The vertical line halfway between the zeros is at x = -1<\/strong>.<\/li>\n\n\n\n
  • Max or Min<\/strong>: The parabola opens downward<\/strong>, so it has a maximum<\/strong>.<\/li>\n\n\n\n
  • Vertex<\/strong>: The vertex is the highest point, located at (-1, 4)<\/strong>.<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Problem 2<\/strong>:<\/h3>\n\n\n\n
      \n
    • Zeros<\/strong>: The graph does not cross<\/strong> the x-axis, so there are no real zeros<\/strong>.<\/li>\n\n\n\n
    • Axis of Symmetry<\/strong>: The parabola is symmetric about the line x = 0<\/strong>.<\/li>\n\n\n\n
    • Max or Min<\/strong>: The parabola opens upward<\/strong>, so it has a minimum<\/strong>.<\/li>\n\n\n\n
    • Vertex<\/strong>: The vertex is at (0, -3)<\/strong>.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Problem 3<\/strong>:<\/h3>\n\n\n\n
        \n
      • Zeros<\/strong>: The parabola crosses the x-axis at x = -4<\/strong> and x = 2<\/strong>.<\/li>\n\n\n\n
      • Axis of Symmetry<\/strong>: The midpoint of the zeros is at x = -1<\/strong>.<\/li>\n\n\n\n
      • Max or Min<\/strong>: It opens upward<\/strong>, so it has a minimum<\/strong>.<\/li>\n\n\n\n
      • Vertex<\/strong>: The vertex lies at (-1, -4)<\/strong>.<\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

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

        Quadratic functions are represented by parabolas on a graph. The zeros<\/strong> of a quadratic function are the x-values where the graph intersects the x-axis, also known as the roots or solutions of the equation. These points occur when the output (y) value is zero.<\/p>\n\n\n\n

        The axis of symmetry<\/strong> is a vertical line that divides the parabola into two mirror-image halves. It always passes through the vertex<\/strong>, which is the highest or lowest point of the graph depending on the direction the parabola opens. You can find the axis of symmetry by averaging the x-values of the two zeros when they exist, using the formula x=x1+x22x = \\frac{x_1 + x_2}{2}x=2×1\u200b+x2\u200b\u200b.<\/p>\n\n\n\n

        The vertex<\/strong> is the turning point of the parabola. If the parabola opens upwards (like a U), the vertex is the minimum point. If it opens downwards (like an upside-down U), the vertex is the maximum point. This tells us whether the function has a maximum or minimum value.<\/p>\n\n\n\n

        In this worksheet, problem 1\u2019s graph has a maximum since it opens down, while problems 2 and 3 have minimums because they open up. Identifying these characteristics helps understand the shape and behavior of quadratic functions, which is useful in solving real-world problems involving area, trajectory, and optimization.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Find zeros, max and min classroom.google.com Algebra 1 8.2 Worksheet Characteristics of Quadratic Functions Name Per____Date____ Determine the value of the zeros, the equation of the axis of symmetry, the max or min value and the vertex. 1. 2. 3. Zeros: Axis of symmetry: Max or Min: Vertex: 4 Zeros: Axis of symmetry: Max or […]<\/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-257464","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257464","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=257464"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257464\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=257464"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=257464"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=257464"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}