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15 y = f(x) is the parabola shown. a Find f(3) and f'(3). b Hence find f(x) in the form f(x) = ax² + bx + c. 14 y=f(x)

15 y = f(x) is the parabola shown. a Find f(3) and f'(3). b Hence find f(x) in the form f(x) = ax² + bx + c. 14 y=f(x)

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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answer question 15 using the graph below

### Problem 15 Given the parabola \( y = f(x) \) as shown in the graph: #### Tasks: **a.** Find \( f(3) \) and \( f'(3) \). **b.** Hence find \( f(x) \) in the form \( f(x) = ax^2 + bx + c \). #### Explanation of the Graph: The graph displays a parabola \( y = f(x) \) with a vertex at the minimum point and a symmetrical shape about the vertical axis. The x-axis and y-axis are labeled. There is a point on the parabola at \( x = 3 \), where the parabola intersects a horizontal line at \( y = 5 \). The tangent to the curve at this point is shown in green crossing the x-axis to the right of the y-axis. The y-axis is marked at intervals, extending up to 14. The goal is to determine the specific value of the function and its derivative at \( x = 3 \) and use this to derive the quadratic function's equation.
Transcribed Image Text:### Problem 15 Given the parabola \( y = f(x) \) as shown in the graph: #### Tasks: **a.** Find \( f(3) \) and \( f'(3) \). **b.** Hence find \( f(x) \) in the form \( f(x) = ax^2 + bx + c \). #### Explanation of the Graph: The graph displays a parabola \( y = f(x) \) with a vertex at the minimum point and a symmetrical shape about the vertical axis. The x-axis and y-axis are labeled. There is a point on the parabola at \( x = 3 \), where the parabola intersects a horizontal line at \( y = 5 \). The tangent to the curve at this point is shown in green crossing the x-axis to the right of the y-axis. The y-axis is marked at intervals, extending up to 14. The goal is to determine the specific value of the function and its derivative at \( x = 3 \) and use this to derive the quadratic function's equation.
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