a Find the zeros and state the multiplicity of each zero b W

a. Find the zeros and state the multiplicity of each zero.

b. Write an? equation, expressed as the product of? factors, of a polynomial function for the graph. Use a leading coefficient of 1 or minus 1 and make the degree of f as small as possible.

c. Use both the equation in part ?(b?) and the graph to find the? y-intercept

.

List the zeros whose multiplicity is even. Select the correct choice below and fill in any answer boxes within your choice.

    A. [ ], ?(Use a comma to separate answers as? needed.)

    B. [ ], There are no such zeros.

List the zeros whose multiplicity is odd. Select the correct choice below and fill in any answer boxes within your choice.

A. [ ], ?(Use a comma to separate answers as? needed.)

B. [ ], There are no such zeros.

b. Write an? equation, expressed as the product of? factors, of a polynomial function for the graph. Use a leading coefficient of 1 or -1 and make the degree of f as small as possible.

?f(x)= [ ], ?(Type your answer in factored? form.)

c. The? y-intercept is [ ].

.

Solution

a) graph crosses x axis at x = - 1 , 2 ----- odd multiplicity

graph touches x axis at x =0 ---- even multiplicity

Overall multiplicity is 4

f(x) = (x+1)(x -2)x^2

y intercept : plug x=0

f(0) = 0

x = 0 ( even multiplicity)

x = - 1 and 2 ( odd multiplicity)