Question

What is the vertex form of `y=-2x^2 + 2x+3`?

Answer 1

`y=(-2)(x-1/2)^2+3 1/2`

Explanation:

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

Given:
`color(white)("XXX")y=-2x^2+2x+3`

Extract the `m` component:
`color(white)("XXX")y=(-2)(x^2-1x)+3`

Complete the square
`color(white)("XXX")y=(-2)(x^2-1x[+(1/2)^2])+3[-(-2)(1/2)^2]`

`color(white)("XXX")y=(-2)(x-1/2)^2+ 3 1/2`

which is the vertex form with vertex at `(1/2, 3 1/2)`

graph{-2x^2+2x+3 [-1.615, 3.86, 1.433, 4.17]}