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Vertex: Axis of symmetry: X f(x) = −(x + 1)² + 2 -10 -8 -6 -4 -2 10- 8- 6- 4 2- -2- -4- -6 -8- F~ 2 4 16 -∞o 8 10

Vertex: Axis of symmetry: X f(x) = −(x + 1)² + 2 -10 -8 -6 -4 -2 10- 8- 6- 4 2- -2- -4- -6 -8- F~ 2 4 16 -∞o 8 10

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Graphing Quadratic Functions #### Problem Statement Graph the function \( f(x) = -(x + 1)^2 + 2 \). Identify the vertex and the axis of symmetry. **Requirements:** - Must show 5 points and axis of symmetry plotted. #### Finding the Vertex and Axis of Symmetry **Vertex:** ___________________ **Axis of symmetry:** _________________ #### Function Table | \( x \) | \( f(x) = -(x + 1)^2 + 2 \) | |--------|-----------------------------| | | | | | | | | | | | | | | | Below the table, you should calculate and input the values for \( x \) and \( f(x) \), using at least five points to plot the function accurately. #### Graph Explanation A coordinate plane is provided where the function can be plotted. - The x-axis ranges from -10 to 10. - The y-axis ranges from -10 to 10. #### Steps to Plot the Function 1. **Identify the Vertex:** - The given function \( f(x) = -(x + 1)^2 + 2 \) is in vertex form, \( f(x) = a(x - h)^2 + k \). - For our function, \( h = -1 \) and \( k = 2 \). - Thus, the vertex is \((-1, 2)\). 2. **Axis of Symmetry:** - The axis of symmetry is a vertical line that passes through the vertex. - For this function, the axis of symmetry is \( x = -1 \). 3. **Calculate Additional Points:** - Choose values for \( x \) around the vertex (e.g., \( x = -3, -2, 0, 1 \)) to find corresponding \( y \)-values using the function \( f(x) = -(x + 1)^2 + 2 \). - Fill in the function table with these calculated points. 4. **Plot the Points:** - Plot the vertex and the additional points on the coordinate plane. - Draw the parabola using these points, ensuring it is symmetric about the axis of symmetry. #### Example Calculation for Additional Points: - When \( x = -3 \): \[ f(-3) = -((-3
Transcribed Image Text:### Graphing Quadratic Functions #### Problem Statement Graph the function \( f(x) = -(x + 1)^2 + 2 \). Identify the vertex and the axis of symmetry. **Requirements:** - Must show 5 points and axis of symmetry plotted. #### Finding the Vertex and Axis of Symmetry **Vertex:** ___________________ **Axis of symmetry:** _________________ #### Function Table | \( x \) | \( f(x) = -(x + 1)^2 + 2 \) | |--------|-----------------------------| | | | | | | | | | | | | | | | Below the table, you should calculate and input the values for \( x \) and \( f(x) \), using at least five points to plot the function accurately. #### Graph Explanation A coordinate plane is provided where the function can be plotted. - The x-axis ranges from -10 to 10. - The y-axis ranges from -10 to 10. #### Steps to Plot the Function 1. **Identify the Vertex:** - The given function \( f(x) = -(x + 1)^2 + 2 \) is in vertex form, \( f(x) = a(x - h)^2 + k \). - For our function, \( h = -1 \) and \( k = 2 \). - Thus, the vertex is \((-1, 2)\). 2. **Axis of Symmetry:** - The axis of symmetry is a vertical line that passes through the vertex. - For this function, the axis of symmetry is \( x = -1 \). 3. **Calculate Additional Points:** - Choose values for \( x \) around the vertex (e.g., \( x = -3, -2, 0, 1 \)) to find corresponding \( y \)-values using the function \( f(x) = -(x + 1)^2 + 2 \). - Fill in the function table with these calculated points. 4. **Plot the Points:** - Plot the vertex and the additional points on the coordinate plane. - Draw the parabola using these points, ensuring it is symmetric about the axis of symmetry. #### Example Calculation for Additional Points: - When \( x = -3 \): \[ f(-3) = -((-3
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