Question

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

Answer 1

`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]}