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.

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