Write a cubic function whose graph is shown. Ay (-5, 0) (4, 0) 8 8 x 4(2,-2) (1, 0) 8. f(x) =
Write a cubic function whose graph is shown. Ay (-5, 0) (4, 0) 8 8 x 4(2,-2) (1, 0) 8. f(x) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Write a Cubic Function Whose Graph is Shown**
The image presents a graph of a cubic function, marked with specific points of interest.
**Graph Description:**
- The graph is plotted on a coordinate plane with the x-axis labeled from -8 to 8 and the y-axis also labeled from -8 to 8.
- The graph crosses the x-axis at three points: (-5, 0), (1, 0), and (4, 0). These points are the roots of the cubic function.
- There is a local maximum near the point (2, 2) on the graph.
- The overall shape of the cubic graph shows it dipping below the x-axis after the root at (-5, 0), peaking near (2, 2), and then rising to pass through the root at (4, 0).
**Function Expression:**
The task is to write the cubic function, \( f(x) \), which could be expressed in factored form using its roots:
\[ f(x) = a(x + 5)(x - 1)(x - 4) \]
To find the specific form of the function, the value of \( a \) would need to be determined, typically using an additional point on the graph. However, such a point is not provided in this transcription.
**Conclusion:**
The function \( f(x) \) is a cubic polynomial with roots at x = -5, 1, and 4. Additional calibration is needed to determine the leading coefficient \( a \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe67f5cb0-daee-4ea8-9bfc-4a00f267029a%2Fd6babe72-6ac5-4af9-b9aa-737f6f6e5629%2Faf6ursq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Write a Cubic Function Whose Graph is Shown**
The image presents a graph of a cubic function, marked with specific points of interest.
**Graph Description:**
- The graph is plotted on a coordinate plane with the x-axis labeled from -8 to 8 and the y-axis also labeled from -8 to 8.
- The graph crosses the x-axis at three points: (-5, 0), (1, 0), and (4, 0). These points are the roots of the cubic function.
- There is a local maximum near the point (2, 2) on the graph.
- The overall shape of the cubic graph shows it dipping below the x-axis after the root at (-5, 0), peaking near (2, 2), and then rising to pass through the root at (4, 0).
**Function Expression:**
The task is to write the cubic function, \( f(x) \), which could be expressed in factored form using its roots:
\[ f(x) = a(x + 5)(x - 1)(x - 4) \]
To find the specific form of the function, the value of \( a \) would need to be determined, typically using an additional point on the graph. However, such a point is not provided in this transcription.
**Conclusion:**
The function \( f(x) \) is a cubic polynomial with roots at x = -5, 1, and 4. Additional calibration is needed to determine the leading coefficient \( a \).
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