Whenever you are given a problem like this, where they give you the roots and degree of a polynomial, start with the factored form of a polynomial. The number of factors is the degree, so Px) will gave three factors:
P(x) = a·(x-p) (x-q) (x-r)
where a is a constant and p, q, and r are the given roots, Since the root 2 has a multiplicity of 2, it appears twice. So the roots are 2, 2, and -3:
P(x) = a·(x-2) (x-2) (x+3)
To find the value of the constant a, plug in the given y-intercept. Note that x = 0 for a y-intercept, so it's (x, y) value is (0, -1.2):
-1.2 = a·(0-2)(0-2)(0+3)
-1.2 = a·12
Solve for a then plug the value back into the equation P(x) = a·(x-2) (x-2) (x+3). You can leave it in factored form. If your teacher wants it in standard form, then you'll need to multiply it out.
