We know the vertex form of a parabola is
y = a(x-h)^2 +k where (h,k) is the vertex
y = a( x-1) ^2+2
We can substitute the point that we are given (3,-6) in for x and y and solve for a
-6 = a(3-1)^2 +2
-6 = a(2)^2+2
-6 = a *4 +2
Subtract 2 from each side
-6 -2 = 4a+2-2
-8 = 4a
Divide each side by 4
-8/4 = 4a/4
-2 =a
y = -2( x-1) ^2+2
The equation is y = -2( x-1) ^2+2
