Construct a polynomial function f with the following characteristics.

Question

Construct a polynomial function f with the following characteristics.

​zeros:

−2​,

2​,

and 4

degree 3

​y-intercept: −32

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Part 1

Choose the correct answer below.

A.

​f(x)=2(x+2)(x−2)(x−4)

B.

​f(x)=−2(x+2)2(x−2)(x−4)

C.

​f(x)=(x+2)(x−2)(x−4)

D.

​f(x)=−2(x+2)(x−2)(x−4)

Answer 1

zeros are 2,-2,4

x=2

x=-2

x=4

x-2=0

x+2=0

x-4=0

are the corresponding 3 factors

multiply the 3 factors together

y = a(x-2)(x+2)(x-4)

plug in the point the y intercept = (0,-32) to solve for "a"

-32 = a(0-2)(0+2)(0-4)= a(-2)(2)(-4)

a = -32/-16 = 2

f(x) = 2(x-2)(x+2)(x-4)

choice A is correct

B has -2(2)=-4 as "a"

C has an implicit 1 as "a"

D has -2 as "a"

A has 2 as "a," 2 is the correct coefficient