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Consider the function g(x) What is the vertex of g ? || g has a Select an answer of The x-intercept(s) of g is/are The y-intercept of g is < Previous T 2 I What is the equation of the line of symmetry of g? C 46 T Graph g(x) 10-9 -8 -7 -6 -5 -4 -3 -2 Clear All Draw: 10 9- 7 6 5 4 3- 2 1 1 2 -3 -4 -5 -6 -7- -8 -9 -10+ 1 4 5 6 789 AVO B 10

Consider the function g(x) What is the vertex of g ? || g has a Select an answer of The x-intercept(s) of g is/are The y-intercept of g is < Previous T 2 I What is the equation of the line of symmetry of g? C 46 T Graph g(x) 10-9 -8 -7 -6 -5 -4 -3 -2 Clear All Draw: 10 9- 7 6 5 4 3- 2 1 1 2 -3 -4 -5 -6 -7- -8 -9 -10+ 1 4 5 6 789 AVO B 10

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 7E
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### Quadratic Function Analysis #### Consider the function \( g(x) = -\frac{1}{4}x^2 - \frac{3}{2}x - \frac{5}{4} \) 1. **What is the vertex of \( g \) ?** - [Text box for students to input the vertex] 2. **What is the equation of the line of symmetry of \( g \) ?** - [Text box for students to input the equation of the line of symmetry] 3. **The function \( g \) has a [Dropdown menu for students to select "maximum" or "minimum"] of** - [Text box for students to input the value of the maximum or minimum] 4. **The \( x \)-intercept(s) of \( g \) is/are** - [Text box for students to input the \( x \)-intercept(s)] 5. **The \( y \)-intercept of \( g \) is** - [Text box for students to input the \( y \)-intercept] #### Graph \( g(x) \) On the right side of the page is a coordinate grid labeled from -10 to 10 on both the x-axis and y-axis. Students are expected to graph the quadratic function \( g(x) = -\frac{1}{4}x^2 - \frac{3}{2}x - \frac{5}{4} \) on this grid. Below the graph, there are drawing tools for students to use: - A straight line tool for drawing asymptotes or lines of symmetry. - A curve tool for sketching quadratic functions. - A point tool for plotting points such as intercepts or vertices. - A circle tool, likely for highlighting important points or regions. Students can use these tools to visually represent their findings on the graph provided. [Navigation buttons for progressing through the educational content, with a "Previous" button to go back to the previous content section.] ### Instructions: - Carefully calculate the vertex, the line of symmetry, and the intercepts before plotting them on the graph. - Utilize the drawing tools provided to accurately represent the quadratic function and its key features. - Double-check your answers for accuracy before moving forward. This exercise aims to develop your skills in analyzing and graphing quadratic functions, reinforcing key concepts in algebra and visual data representation.
Transcribed Image Text:### Quadratic Function Analysis #### Consider the function \( g(x) = -\frac{1}{4}x^2 - \frac{3}{2}x - \frac{5}{4} \) 1. **What is the vertex of \( g \) ?** - [Text box for students to input the vertex] 2. **What is the equation of the line of symmetry of \( g \) ?** - [Text box for students to input the equation of the line of symmetry] 3. **The function \( g \) has a [Dropdown menu for students to select "maximum" or "minimum"] of** - [Text box for students to input the value of the maximum or minimum] 4. **The \( x \)-intercept(s) of \( g \) is/are** - [Text box for students to input the \( x \)-intercept(s)] 5. **The \( y \)-intercept of \( g \) is** - [Text box for students to input the \( y \)-intercept] #### Graph \( g(x) \) On the right side of the page is a coordinate grid labeled from -10 to 10 on both the x-axis and y-axis. Students are expected to graph the quadratic function \( g(x) = -\frac{1}{4}x^2 - \frac{3}{2}x - \frac{5}{4} \) on this grid. Below the graph, there are drawing tools for students to use: - A straight line tool for drawing asymptotes or lines of symmetry. - A curve tool for sketching quadratic functions. - A point tool for plotting points such as intercepts or vertices. - A circle tool, likely for highlighting important points or regions. Students can use these tools to visually represent their findings on the graph provided. [Navigation buttons for progressing through the educational content, with a "Previous" button to go back to the previous content section.] ### Instructions: - Carefully calculate the vertex, the line of symmetry, and the intercepts before plotting them on the graph. - Utilize the drawing tools provided to accurately represent the quadratic function and its key features. - Double-check your answers for accuracy before moving forward. This exercise aims to develop your skills in analyzing and graphing quadratic functions, reinforcing key concepts in algebra and visual data representation.
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