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Find the equation of the quadratic function f whose graph is shown below. 6+ (1, 5) f(4) = 0 -8 -4 -2 10 (3,-3) 4- -10-+

Find the equation of the quadratic function f whose graph is shown below. 6+ (1, 5) f(4) = 0 -8 -4 -2 10 (3,-3) 4- -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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### Writing the Equation of a Quadratic Function Given Its Graph **Task:** Find the equation of the quadratic function \( f \) whose graph is shown below. **Graph Analysis:** - The graph is a parabola that opens downward. - It is plotted on a coordinate grid. - The parabola passes through the points \( (1, 5) \) and \( (3, -3) \). - The vertex, which is the highest point for this downward-opening parabola, is visible but the coordinates are not given explicitly in the image. **Equation Form:** The equation of a quadratic function is typically in the form: \[ f(x) = ax^2 + bx + c \] **Steps to Determine the Equation:** 1. Identify key points on the graph, such as the vertex and any other points the parabola passes through. 2. Use these points to set up a system of equations to solve for the coefficients \( a \), \( b \), and \( c \). 3. Substitute these values into the standard quadratic form. **Interactive Element:** There is a box next to \( f(x) = \) where the final equation can be entered. **Additional Features:** - There are options for further explanations and checking the answer provided at the bottom of the page.
Transcribed Image Text:### Writing the Equation of a Quadratic Function Given Its Graph **Task:** Find the equation of the quadratic function \( f \) whose graph is shown below. **Graph Analysis:** - The graph is a parabola that opens downward. - It is plotted on a coordinate grid. - The parabola passes through the points \( (1, 5) \) and \( (3, -3) \). - The vertex, which is the highest point for this downward-opening parabola, is visible but the coordinates are not given explicitly in the image. **Equation Form:** The equation of a quadratic function is typically in the form: \[ f(x) = ax^2 + bx + c \] **Steps to Determine the Equation:** 1. Identify key points on the graph, such as the vertex and any other points the parabola passes through. 2. Use these points to set up a system of equations to solve for the coefficients \( a \), \( b \), and \( c \). 3. Substitute these values into the standard quadratic form. **Interactive Element:** There is a box next to \( f(x) = \) where the final equation can be entered. **Additional Features:** - There are options for further explanations and checking the answer provided at the bottom of the page.
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