It's best to actually write out the equation for this parabola. The vertex form of the equation of a parabola is y-k=a(x-h)^2.
Given that the vertex of our parabola is (6,27), the equation becomes
y-27 = a(x-6)^2.
We are also told that the y-intercept is (0, -81). Substituting 0 for x and -81 for y, we get
-81-27 = a (0-6)^2. Solve for a: -108 = a(36), so a = -3
Then the equation of our parabola is y-27 = -3(x-6)^2.