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: [tex]y=a(x-h) ^{2}+k [/tex] 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: [tex]-9=a(-8-1) ^{2} +6[/tex]. 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 [tex]y=- \frac{5}{27}(x-1) ^{2}+6 [/tex]
