What is the vertex form of y=-x^2+2x-2?

1 Answer
Feb 5, 2016

y=(-1)(x-1)^2+(-1)

Explanation:

The general vertex form is
color(white)("XXX")y=m(x-a)^2+b with vertex at (a,b)

Given
color(white)("XXX")y=-x^2+2x-2

color(white)("XXX")y=(-1)(x^2-2x+2)

color(white)("XXX")y=(-1)(x^2-2x+1+1)

color(white)("XXX")y=(-1)(x^2-2x+1)-1

color(white)("XXX")y=(-1)(x-1)^2 + (-1)

which is the vertex form with m=(-1), a=1, and b=(-1)
graph{-x^2+2x-2 [-3.215, 6.65, -4.532, 0.4]}