{"id":278312,"date":"2025-08-02T02:59:53","date_gmt":"2025-08-02T02:59:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=278312"},"modified":"2025-08-02T02:59:54","modified_gmt":"2025-08-02T02:59:54","slug":"parent-functions-transformations-bell","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/02\/parent-functions-transformations-bell\/","title":{"rendered":"Parent Functions & Transformations Bell"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Here are the correct answers and the explanation for the problem shown in the image.
Answers:
Minimum \/ Maximum: Minimum
Axis of Symmetry: x = 4
Vertex: (4, 1)
Domain: (-\u221e, \u221e)
Range: [1, \u221e)
Table of Values:
x=2, f(x)=5
x=3, f(x)=2
x=4, f(x)=1
x=5, f(x)=2
x=6, f(x)=5
Explanation
The problem asks for a complete analysis of the quadratic function f(x) = x\u00b2 – 8x + 17. This function is in the standard form f(x) = ax\u00b2 + bx + c, where a = 1, b = -8, and c = 17.
First, we determine if the function has a minimum or a maximum value. This is dictated by the coefficient ‘a’. Since ‘a’ is 1, which is a positive number, the parabola opens upwards. A parabola that opens upwards has a lowest point, so the function has a minimum value.
Next, we find the axis of symmetry, which is the vertical line that divides the parabola into two mirror images. The formula for the axis of symmetry is x = -b \/ (2a). Plugging in our values, we get x = -(-8) \/ (2 * 1), which simplifies to x = 8 \/ 2, so the axis of symmetry is the line x = 4.
The vertex is the turning point of the parabola and it lies on the axis of symmetry. We already have its x-coordinate, which is 4. To find the y-coordinate, we substitute this x-value back into the function: f(4) = (4)\u00b2 – 8(4) + 17. This calculates to f(4) = 16 – 32 + 17, which equals 1. Therefore, the vertex is located at the point (4, 1).
To graph the function, we create a table of values centered around the vertex. We already know the point (4, 1). We can choose x-values on either side of 4, such as 3 and 5. For x=3, f(3) = (3)\u00b2 – 8(3) + 17 = 9 – 24 + 17 = 2. Due to symmetry, the value for x=5 will also be 2. These points, (3, 2) and (5, 2), can be plotted.
The domain of a quadratic function is the set of all possible x-values. Since you can substitute any real number for x, the domain is all real numbers, expressed in interval notation as (-\u221e, \u221e).
The range is the set of all possible y-values. Since the parabola opens upwards from its minimum point at the vertex (4, 1), the lowest y-value is 1. The y-values then extend infinitely upwards. The range is therefore all real numbers greater than or equal to 1, written as [1, \u221e).<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: Here are the correct answers and the explanation for the problem shown in the image.Answers:Minimum \/ Maximum: MinimumAxis of Symmetry: x = 4Vertex: (4, 1)Domain: (-\u221e, \u221e)Range: [1, \u221e)Table of Values:x=2, f(x)=5x=3, f(x)=2x=4, f(x)=1x=5, f(x)=2x=6, f(x)=5ExplanationThe problem asks for a complete analysis of the quadratic function f(x) = x\u00b2 […]<\/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-278312","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278312","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=278312"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278312\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=278312"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=278312"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=278312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}