-2x^2 +4x = 6
One pre-requisite of completing the square is to have the coefficient of the squared term to be 1. So factor out a -2.
-2(x^2-2x) = 6
-2(x^2-2x+1) = 6+-2(1) (completing the square step since (-2/2)^2 = 1
-2(x-1)^2 = 4 (since x^2-2x+1 is (x-1)^2)
-2(x-1)^2 - 4 is our vertex form.
Notice this satisfies our a(x-h)^2 + k form.
To check:
In general for ax^2+bx+c where our vertex is (h,k), we have that
a = -2
h = -b/2a = -4 / -4 = 1
k = f(h) = f(1) = -2+4-6 = -4
So our a(x-h)^2 +k could have been done in this fashion since a = -2, h = 1, k = -4 hence -2(x-1)^2 -4
