help with graphs please

[sungjin6458]

construct a polynomial funtion with these:
intercepts at (-3,0)(-1,0) (3,0)this one is double root
y intercept at (0,-5)

i did:
f(x)=(x+1)(x+3)(x-3)^2
and got f(x)=x^4-2x^3-12x^2 +18x+22..but it was wrong..help pleaz[/img]

 

[Unco]

You are correct that
f(x)=(x+1)(x+3)(x-3)^2 fits the root description.

However, so does
f(x)=2(x+1)(x+3)(x-3)^2
or f(x)=10(x+1)(x+3)(x-3)^2

or any other function where we stick in a constant, call it k:
f(x)=k(x+1)(x+3)(x-3)^2

Now use the y-intercept (ie. the known point (0,-5)) to find k.