Which polynomial function is graphed below ??
A.) f(x)=(x-3)(x+3)^2
B.) f(x)=(x-2)^2(x+3)
C.)f(x)=(x13)^2(x+2)
D.) f(x)=(x-2)(x+3)^2

f(x)=(x-3)(x+2)^2

Step-by-step explanation:

If x=3, f(3)=0, (1)

if x=-2, f(-2)=0 (2)

f(0)=-12 (3)

From (1),(2) and (3):

The null functions are 3 and - 2, which is why :f(x) =(x-3)(x -(-2)) =(x-3)(x+2)

From (3): f(0)=-12 then (x+2) must be on squared, then

f(x) =(x-3)(x+2)^2

Really: f(0)=(0-3)(0+2)^2 =-3*2^2=-3*4=-12