What are the x intercepts of a parabola with vertex (6,27) and y intercept of (0.-81) ?

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.