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Determine an equation for the pictured graph. Write your answer in factored form and assume the leading coefficient is either 1 or -1, you should be able to determine which is the case by looking at the graph. -B 8 7 6 5 4 3 2

Determine an equation for the pictured graph. Write your answer in factored form and assume the leading coefficient is either 1 or -1, you should be able to determine which is the case by looking at the graph. -B 8 7 6 5 4 3 2

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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**Task: Determine an Equation** Determine an equation for the pictured graph. Write your answer in factored form and assume the leading coefficient is either 1 or -1. You should be able to determine which is the case by looking at the graph. **Graph Analysis** The graph is a cubic function that crosses the x-axis at three points, indicating it has three real roots. The general shape appears to be a typical cubic curve. Here are some observations: - The x-intercepts, based on the grid, are approximately at x = -3, x = -1, and x = 2. - The graph shows a downward opening on the left side and an upward opening on the right side, suggesting a positive leading coefficient. - The point where the graph changes direction suggests that it is of odd degree. **Conclusion** Given these observations, one possible factored form of the equation could be: \[ y = (x + 3)(x + 1)(x - 2) \] If a negative leading coefficient were to be considered based on graph orientation, the equation might need to be: \[ y = -(x + 3)(x + 1)(x - 2) \] However, the orientation observed suggests the positive leading coefficient is more likely.
Transcribed Image Text:**Task: Determine an Equation** Determine an equation for the pictured graph. Write your answer in factored form and assume the leading coefficient is either 1 or -1. You should be able to determine which is the case by looking at the graph. **Graph Analysis** The graph is a cubic function that crosses the x-axis at three points, indicating it has three real roots. The general shape appears to be a typical cubic curve. Here are some observations: - The x-intercepts, based on the grid, are approximately at x = -3, x = -1, and x = 2. - The graph shows a downward opening on the left side and an upward opening on the right side, suggesting a positive leading coefficient. - The point where the graph changes direction suggests that it is of odd degree. **Conclusion** Given these observations, one possible factored form of the equation could be: \[ y = (x + 3)(x + 1)(x - 2) \] If a negative leading coefficient were to be considered based on graph orientation, the equation might need to be: \[ y = -(x + 3)(x + 1)(x - 2) \] However, the orientation observed suggests the positive leading coefficient is more likely.
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