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Find the equation of this particular 5th degree polynomial that goes through the point (-1, 72). - -2 -1 90- 72- 54- 36- 18- -18- -36- -54- -72- L90 3

Find the equation of this particular 5th degree polynomial that goes through the point (-1, 72). - -2 -1 90- 72- 54- 36- 18- -18- -36- -54- -72- L90 3

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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**Title: Analyzing a 5th Degree Polynomial** **Objective:** Find the equation of the given 5th degree polynomial that passes through the point (-1, 72). **Description:** This task involves identifying the equation of a specific 5th degree polynomial graph. The polynomial passes through the highlighted point (-1, 72) on the graph. **Graph Explanation:** - **Axes:** The graph is plotted on a Cartesian coordinate system with the x-axis ranging from -5 to 5 and the y-axis ranging from -90 to 90. - **Polynomial Curve:** The blue curve represents the 5th degree polynomial. It exhibits typical characteristics of such polynomials, including multiple turns and changes in direction. - **Key Point:** The graph passes through the point (-1, 72), which is marked on the plot. This indicates that when x = -1, the y-value of the polynomial is 72. - **Behavior:** The curve demonstrates several peaks and troughs as expected for higher-degree polynomials. It crosses the x-axis multiple times, signifying the roots of the polynomial. **Analysis:** To find the polynomial equation, consider both the degree and the requirement to pass through the specific point. Techniques such as polynomial fitting, system of equations, or using specific software tools can be applied to determine the complete equation that satisfies these conditions. By analyzing the graph and applying mathematical concepts, you can successfully identify the function that models this polynomial accurately.
Transcribed Image Text:**Title: Analyzing a 5th Degree Polynomial** **Objective:** Find the equation of the given 5th degree polynomial that passes through the point (-1, 72). **Description:** This task involves identifying the equation of a specific 5th degree polynomial graph. The polynomial passes through the highlighted point (-1, 72) on the graph. **Graph Explanation:** - **Axes:** The graph is plotted on a Cartesian coordinate system with the x-axis ranging from -5 to 5 and the y-axis ranging from -90 to 90. - **Polynomial Curve:** The blue curve represents the 5th degree polynomial. It exhibits typical characteristics of such polynomials, including multiple turns and changes in direction. - **Key Point:** The graph passes through the point (-1, 72), which is marked on the plot. This indicates that when x = -1, the y-value of the polynomial is 72. - **Behavior:** The curve demonstrates several peaks and troughs as expected for higher-degree polynomials. It crosses the x-axis multiple times, signifying the roots of the polynomial. **Analysis:** To find the polynomial equation, consider both the degree and the requirement to pass through the specific point. Techniques such as polynomial fitting, system of equations, or using specific software tools can be applied to determine the complete equation that satisfies these conditions. By analyzing the graph and applying mathematical concepts, you can successfully identify the function that models this polynomial accurately.
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