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2. Write an equation and sketch a graph of a polynomial function that has 3 roots, 2 with even multiplicities, and that has end behavior f (x) → 0o as x -→ -0o and f(x) = -00 as x → o. Note: You can check your answer using Desmos.

2. Write an equation and sketch a graph of a polynomial function that has 3 roots, 2 with even multiplicities, and that has end behavior f (x) → 0o as x -→ -0o and f(x) = -00 as x → o. Note: You can check your answer using Desmos.

Algebra and Trigonometry (6th Edition)
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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Certainly! Below is the transcription of the image suitable for an educational website: --- **Question 2:** Write an equation and sketch a graph of a polynomial function that has 3 roots, 2 with even multiplicities, and that has end behavior \( f(x) \to \infty \) as \( x \to -\infty \) and \( f(x) \to -\infty \) as \( x \to \infty \). Note: You can check your answer using Desmos. **Graph Paper:** The background is a grid with horizontal and vertical lines, forming a series of squares. This setup can be utilized to sketch the polynomial function graph. **Instructions for Graphing:** 1. Identify three roots for the polynomial. Assume two roots have even multiplicities. For example, let's consider roots at \( x = -2, 0, \) and \( 2 \), where the roots at \( x = -2 \) and \( x = 2 \) have multiplicity 2. 2. Write the polynomial equation: \( f(x) = c(x + 2)^2(x)(x - 2)^2 \). 3. Choose the coefficient \( c \) to match the end behavior conditions as specified in the prompt. 4. Carefully plot the curve on the grid, making sure to reflect the roots and their multiplicities appropriately, ensuring the polynomial demonstrates the specified end behavior. **Note:** Utilize graphing tools like Desmos to verify the correctness of your polynomial function graph.
Transcribed Image Text:Certainly! Below is the transcription of the image suitable for an educational website: --- **Question 2:** Write an equation and sketch a graph of a polynomial function that has 3 roots, 2 with even multiplicities, and that has end behavior \( f(x) \to \infty \) as \( x \to -\infty \) and \( f(x) \to -\infty \) as \( x \to \infty \). Note: You can check your answer using Desmos. **Graph Paper:** The background is a grid with horizontal and vertical lines, forming a series of squares. This setup can be utilized to sketch the polynomial function graph. **Instructions for Graphing:** 1. Identify three roots for the polynomial. Assume two roots have even multiplicities. For example, let's consider roots at \( x = -2, 0, \) and \( 2 \), where the roots at \( x = -2 \) and \( x = 2 \) have multiplicity 2. 2. Write the polynomial equation: \( f(x) = c(x + 2)^2(x)(x - 2)^2 \). 3. Choose the coefficient \( c \) to match the end behavior conditions as specified in the prompt. 4. Carefully plot the curve on the grid, making sure to reflect the roots and their multiplicities appropriately, ensuring the polynomial demonstrates the specified end behavior. **Note:** Utilize graphing tools like Desmos to verify the correctness of your polynomial function graph.
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