Use the graph to identify the formula for a polynomial function of least degree. y 5- 4- 2 1+ +►X -5 -4 -3 2 -i 0 -1+ 1 2 3 4 5 -2- -3- -4 -5+
Use the graph to identify the formula for a polynomial function of least degree. y 5- 4- 2 1+ +►X -5 -4 -3 2 -i 0 -1+ 1 2 3 4 5 -2- -3- -4 -5+
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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How would you found the equation ?
Transcribed Image Text:**Graph Description for Identifying the Polynomial Function of Least Degree**
The image presents a graph of a polynomial function. The graph is plotted on a Cartesian coordinate system with the horizontal axis labeled as \(x\) and the vertical axis labeled as \(y\). The graph exhibits the following characteristics:
1. **Intercepts:**
- The graph crosses the x-axis at three points: approximately \(x = -3\), \(x = 1\), and \(x = 4\).
2. **Turning Points:**
- The graph shows three turning points, suggesting a polynomial with at least a degree of four. It peaks around \(x = -2\) and \(x = 2\), and there is a trough between these peaks.
3. **End Behavior:**
- As \(x\) approaches \(-\infty\) and \(+\infty\), the value of \(y\) approaches \(+\infty\), indicating that the polynomial has an even degree.
4. **General Shape:**
- The graph suggests a polynomial function with a degree of four because of its three turning points and the behavior described.
Based on these observations, the polynomial function of least degree that fits this graph would likely be a quartic polynomial of the form \(y = ax^4 + bx^3 + cx^2 + dx + e\).
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