The coordinates of the vertex are (h,k) = (-3,2), so the quadratic equation becomes:

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

We can use the y-intercept to find the value of "a."

We have that f(0) = 4:

4 = a(0 + 3)^2 + 2 = 9a + 2

9a = 2

a = 2/9

Therefore, the equation becomes:

f(x) = 2/9(x + 3)^2 + 2