# Analyzing a Polynomial Function

Please see the attached file for the fully formatted problems.

Find a polynomial function for the attached graph and find the solutions to the following parts.

A. How many zeros does the function have? What are their multiplicities?

B. Construct a polynomial function whose zeros are those identified in Part A. What role does the multiplicity play in determining the factors? Graph the function using a graphing utility.

C. Is the leading coefficient of the polynomial positive or negative? Why?

D. What is the y-intercept of P?

E. Construct a polynomial function whose zeros are those determined in Part A and whose y-intercept is the one determined in Part D.

F. Find the power function that the graph of the function resembles for large values of |x|.

G. Find a second function that "fits" the graph. Be sure to check its graph on your graphing utility. What similarities do you find between the two functions? What differences do you find?

H. Write a general polynomial in its factored form whose graph could look like the one given, based on the four points specified. Be sure to state any conditions on the factors and give a general formula for the leading coefficient.

https://brainmass.com/math/graphs-and-functions/analyzing-polynomial-function-6829

#### Solution Preview

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Solution:

(A) The function cuts the x-axis 3 times and it is tangential once therefore it has five zeros.

Only one is in double form.

(B) From graph we have value of y =0 at

x = -6 ,x = -4 , x = -2 ...

#### Solution Summary

This solution is provided within an attached Word document and all responses are detailed in relation to the provided polynomial graph. A function that fits the graph is also found.