You can use the given info to build a system and then solve for the coefficients.

The y-intercept is 9, therefore, x=0:

A root is -3:

Passes through (-2,3):

Passes through (1,16):

Now, you have 4 equations with 4 unknowns:

Solve the system and you get:

Therefore, the polynomial is:

This is one way to approach these. Perhaps try this on your other post regarding the quartic.