You are given the coordinates of the vertex (1,6) and of a point (-8,-9) on a parabola. find the equation of the parabola.

We know this is an upside down parabola because the vertex is higher than the point.  So it will have a negative leading coefficient or "a" value. We have this then as our standard form: where h and k are the coordinates of the vertex and x and y are the coordinates of the point.  We will fill in our standard equation with those values and solve for a, then rewrite.  Here's what we have so far: .  Simplifying that will give us -9=a(81)+6.  Subtract 6 from both sides and we solve to find that a=-5/27.  See, that's how we know it's upside down.  Our a value is solved as a negative.  Now, put that value of a back in along with the vertex to get a final equation of