a. Find the zeros and state the multiplicity of each zero. b. Write an? equation

Question

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 [ ].

.

Explanation / Answer

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)

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