y=-3x^2+12x?

Question

we have to write it in vertex form, and then identity the vertex and axis of symmetry and the direction of opening.

Answer 1

Factor out a -3: x^2 -4x
Complete the square: x^2 -4x +(-2)^2
Finally: -3[(x-2)^2 -4], so the vertex is (2,12)
axis of symmetry is x=2 ( x-2 =0, so x=2)
and, because of the negative sign in front, it opens down