**Instruction:**Find an equation for the graph of the degree 5 polynomial function shown below. Leave the function in factored form.**Graph Description:**The graph represents a degree 5 polynomial function. It crosses the x-axis at approximately \( x = -3, x = -1, x = 0, x = 1.5, \) and \( x = 3 \). These are the approximate roots of the polynomial. The curve shows complex behavior with multiple turns, characteristic of higher-degree polynomials.- The graph dips below the x-axis before rising steeply upwards to a peak.- It then descends towards a trough above the x-axis, before climbing again to another peak.- The graph finally falls steeply, crossing the x-axis at around \( x = 3 \).This complex behavior is typical of a polynomial with degree five, as it can have up to four turning points.**Guidance:**To write the equation of the polynomial, identify the roots \( (-3, -1, 0, 1.5, 3) \) and construct factors such as \( (x + 3), (x + 1), x, (x - 1.5), (x - 3) \). Note that leading coefficients and multiplicity (if roots are repeated) also impact the polynomial's shape, and the curve's orientation signifies the sign of the leading coefficient. Adjust these factors to fit the graph, ensuring that it accurately reflects the intercepts and turning points.

Answered: Find an equation for the graph of the…

Find an equation for the graph of the degree 5 polynomial function shown below. Leave the function in factored form 36 32 30 28 26 24 22 20 16 12 10

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Instruction:**

Find an equation for the graph of the degree 5 polynomial function shown below. Leave the function in factored form.

**Graph Description:**

The graph represents a degree 5 polynomial function. It crosses the x-axis at approximately \( x = -3, x = -1, x = 0, x = 1.5, \) and \( x = 3 \). These are the approximate roots of the polynomial. The curve shows complex behavior with multiple turns, characteristic of higher-degree polynomials.

- The graph dips below the x-axis before rising steeply upwards to a peak.
- It then descends towards a trough above the x-axis, before climbing again to another peak.
- The graph finally falls steeply, crossing the x-axis at around \( x = 3 \).

This complex behavior is typical of a polynomial with degree five, as it can have up to four turning points.

**Guidance:**

To write the equation of the polynomial, identify the roots \( (-3, -1, 0, 1.5, 3) \) and construct factors such as \( (x + 3), (x + 1), x, (x - 1.5), (x - 3) \). Note that leading coefficients and multiplicity (if roots are repeated) also impact the polynomial's shape, and the curve's orientation signifies the sign of the leading coefficient. Adjust these factors to fit the graph, ensuring that it accurately reflects the intercepts and turning points.

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