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5. Given graph of the 4th degree function. a) Identify zeros b) Write a formula for a possible polynomial function that the graph represents using c as the constant factor. c) Use the y-intercept of the function to find c. d) Write the function in standard form. 10 0

5. Given graph of the 4th degree function. a) Identify zeros b) Write a formula for a possible polynomial function that the graph represents using c as the constant factor. c) Use the y-intercept of the function to find c. d) Write the function in standard form. 10 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Educational Resource on Polynomial Functions #### 5. Analysis of a 4th Degree Polynomial Function Graph **a) Identify the Zeros:** Examine the points where the graph intersects the x-axis to determine the zeros of the function. **b) Write a Formula:** Craft a possible polynomial equation that aligns with the graph, incorporating \( c \) as the constant factor. **c) Determine Constant \( c \):** Utilize the y-intercept, where the graph crosses the y-axis, to solve for the value of \( c \). **d) Function in Standard Form:** Express the derived polynomial function in standard form, arranging terms by descending order of power. #### Graph Analysis - **Axes and Plot Range:** - The graph displays a red polynomial curve. - The x-axis ranges approximately from \(-3\) to \(3\). - The y-axis ranges from around \(-15\) to \(15\). - **Graph Features:** - The polynomial curve intersects the x-axis at several points, indicating the zeros of the function. - The graph showcases the typical shape expected of a quartic (4th degree) polynomial, with multiple turns corresponding to changes in direction. - **Major Points and Behavior:** - The curve's behavior is indicative of the properties of polynomial functions, such as end behavior associated with even-degree functions.
Transcribed Image Text:### Educational Resource on Polynomial Functions #### 5. Analysis of a 4th Degree Polynomial Function Graph **a) Identify the Zeros:** Examine the points where the graph intersects the x-axis to determine the zeros of the function. **b) Write a Formula:** Craft a possible polynomial equation that aligns with the graph, incorporating \( c \) as the constant factor. **c) Determine Constant \( c \):** Utilize the y-intercept, where the graph crosses the y-axis, to solve for the value of \( c \). **d) Function in Standard Form:** Express the derived polynomial function in standard form, arranging terms by descending order of power. #### Graph Analysis - **Axes and Plot Range:** - The graph displays a red polynomial curve. - The x-axis ranges approximately from \(-3\) to \(3\). - The y-axis ranges from around \(-15\) to \(15\). - **Graph Features:** - The polynomial curve intersects the x-axis at several points, indicating the zeros of the function. - The graph showcases the typical shape expected of a quartic (4th degree) polynomial, with multiple turns corresponding to changes in direction. - **Major Points and Behavior:** - The curve's behavior is indicative of the properties of polynomial functions, such as end behavior associated with even-degree functions.
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