**Title: Finding a Degree 3 Polynomial****Task:**Find the polynomial $ P(x) $ of degree 3 whose graph is shown.**Graph Description:**- The graph is plotted on a Cartesian coordinate system with both x-axis and y-axis ranging from -5 to 5.- The polynomial graph is a smooth curve passing through the following key points: - The curve rises from the left, reaching a local maximum near (-2, 2). - It then descends, crossing the x-axis near $ x = 0 $. - A local minimum is observed near (1, -4). - The curve continues upward beyond the x-axis on the right side.**Characteristics of the Graph:**- **Local Maximum**: Approximately at $ x = -2 $.- **Local Minimum**: Approximately at $ x = 1 $.- **X-Intercepts**: Around $ x = 0 $.- The graph is symmetric in terms of rising and falling, typical of cubic functions.**Understanding the Graph:**- The leading coefficient is positive, indicated by the graph’s rise on the right side.- The polynomial’s roots can be estimated by observing the x-intercepts.- The turning points relate closely to the derivative of the cubic polynomial equation.**Next Steps:**To find the specific polynomial function $ P(x) $, use the key points and solve for variables in the general cubic equation form $ P(x) = ax^3 + bx^2 + cx + d $. Utilize methods such as polynomial fitting or algebraic manipulation for exact calculations.

The given graph touches or cut the x-axis at x=-2, x=-2 and x=1 So the zero’s of the polynomials…

Answered: Find the polynomial P( x) of the degree…

Math

Calculus

Find the polynomial P( x) of the degree 3 whose graph is shown. 5 4 2+ -5 -4 -3 -2 3 4 -1 -2+ -3+ -4 2- LO

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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**Title: Finding a Degree 3 Polynomial**

**Task:**
Find the polynomial $ P(x) $ of degree 3 whose graph is shown.

**Graph Description:**
- The graph is plotted on a Cartesian coordinate system with both x-axis and y-axis ranging from -5 to 5.
- The polynomial graph is a smooth curve passing through the following key points:
- The curve rises from the left, reaching a local maximum near (-2, 2).
- It then descends, crossing the x-axis near $ x = 0 $.
- A local minimum is observed near (1, -4).
- The curve continues upward beyond the x-axis on the right side.

**Characteristics of the Graph:**
- **Local Maximum**: Approximately at $ x = -2 $.
- **Local Minimum**: Approximately at $ x = 1 $.
- **X-Intercepts**: Around $ x = 0 $.
- The graph is symmetric in terms of rising and falling, typical of cubic functions.

**Understanding the Graph:**
- The leading coefficient is positive, indicated by the graph’s rise on the right side.
- The polynomial’s roots can be estimated by observing the x-intercepts.
- The turning points relate closely to the derivative of the cubic polynomial equation.

**Next Steps:**
To find the specific polynomial function $ P(x) $, use the key points and solve for variables in the general cubic equation form $ P(x) = ax^3 + bx^2 + cx + d $. Utilize methods such as polynomial fitting or algebraic manipulation for exact calculations.

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