Question

What is the vertex form of `y=(-x - 1) (x - 3)`?

Answer 1

`y=(-1)(x-1)^2+4`
`color(white)("XXXXXXXXXXX")`with vertex at `(1,4)`

Explanation:

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

Given
`color(white)("XXX")y=(-x-1)(x-3)`

`color(white)("XXXy")=(-`1)(x+1)(x-3)`

`color(white)("XXXy")=(-1)(x^2-2x-3)`

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

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

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

`color(white)("XXX")`which is in vertex form

graph{(-x-1)(x-3) [-2.986, 8.11, -0.613, 4.934]}