How would you found the equation ? **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 $y = ax^4 + bx^3 + cx^2 + dx + e$.

1. Identify the x-intercepts from the graph In the above graph the x intercepts are at x=-4 , x=-2…

Answered: Use the graph to identify the formula…

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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

How would you found the equation ?

**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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