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y| (-5,0) (-2,0) (2,0) -6 -4 -3 -2 2 3. (0,-4) Graph of a Polynomial Function -10 -20 Given above is the graph of a polynomial function P(x). Please select all factors of P(x).

y| (-5,0) (-2,0) (2,0) -6 -4 -3 -2 2 3. (0,-4) Graph of a Polynomial Function -10 -20 Given above is the graph of a polynomial function P(x). Please select all factors of P(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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### Question Completion Status: #### QUESTION 13 [Graph of a Polynomial Function] **Description:** The graph displayed is of a polynomial function \(P(x)\). The horizontal axis (x-axis) and vertical axis (y-axis) are marked. There are specific points labeled on the graph as follows: - \((-5, 0)\) - \((-2, 0)\) - \((0,-4)\) - \((2, 0)\) The curve shows the polynomial crossing the x-axis at three points: \((-5, 0)\), \((-2, 0)\), and \((2, 0)\). These points are the roots or zeroes of the polynomial. Additionally, the curve touches the minimum point at approximately \((0, -4)\). **Instructions:** Given above is the graph of a polynomial function \(P(x)\). Please select all factors of \(P(x)\). **Submission Instructions:** Click "Save and Submit" to save and submit. Click "Save All Answers" to save all answers. **Graph Analysis:** - The roots of the polynomial signify the x-values where \(P(x) = 0\). These points are where the graph intersects the x-axis. - The turning point at \((0, -4)\) indicates a local minimum for the polynomial function. - The behavior of the graph suggests a polynomial of at least fourth degree, given the two local turning points and three x-intercepts. Students should analyze the graph, identify potential polynomial factors corresponding to the roots, and calculate or estimate the polynomial’s equation based on the information provided on the graph. **Note:** In practical application, polynomials can have complex factors, and higher-degree polynomials especially require careful calculation for accurate factorization. Make sure to cross-check your selected factors with the polynomial's given behavior and known roots.
Transcribed Image Text:### Question Completion Status: #### QUESTION 13 [Graph of a Polynomial Function] **Description:** The graph displayed is of a polynomial function \(P(x)\). The horizontal axis (x-axis) and vertical axis (y-axis) are marked. There are specific points labeled on the graph as follows: - \((-5, 0)\) - \((-2, 0)\) - \((0,-4)\) - \((2, 0)\) The curve shows the polynomial crossing the x-axis at three points: \((-5, 0)\), \((-2, 0)\), and \((2, 0)\). These points are the roots or zeroes of the polynomial. Additionally, the curve touches the minimum point at approximately \((0, -4)\). **Instructions:** Given above is the graph of a polynomial function \(P(x)\). Please select all factors of \(P(x)\). **Submission Instructions:** Click "Save and Submit" to save and submit. Click "Save All Answers" to save all answers. **Graph Analysis:** - The roots of the polynomial signify the x-values where \(P(x) = 0\). These points are where the graph intersects the x-axis. - The turning point at \((0, -4)\) indicates a local minimum for the polynomial function. - The behavior of the graph suggests a polynomial of at least fourth degree, given the two local turning points and three x-intercepts. Students should analyze the graph, identify potential polynomial factors corresponding to the roots, and calculate or estimate the polynomial’s equation based on the information provided on the graph. **Note:** In practical application, polynomials can have complex factors, and higher-degree polynomials especially require careful calculation for accurate factorization. Make sure to cross-check your selected factors with the polynomial's given behavior and known roots.
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