Discuss the below:
Q: Find a polynomial function for the of the form P(x)=anxn+an-1xn-1+.......+a0 defined by graph illustrated
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.