Question

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

Answer 1

`y=(-1)(x-(-1))^2+4`

Explanation:

The vertex form of a quadratic is
`color(white)("XXX")y=m(x-color(red)(a))^2+color(blue)(b)color(white)("XXX")`with vertex at `(color(red)(a),color(blue)(b))`

Given `y=-x^2-2x+3`

Extract the `m` factor from the terms including an `x`
`color(white)("XXX")y= (-1)(x^2+2x) +3`

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

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

`color(white)("XXX")y=(-1)(x+1)^2 + 4`

`color(white)("XXX")y=(-1)(x-(color(red)(-1)))^2+color(blue)(4)`
which is the graph{-x^2-2x+3 [-6.737, 5.753, -0.565, 5.675]} vertex form with vertex at `(color(red)(-1),color(blue)(4))`