Question

What is the vertex form of `y=x^2-4x-3`?

Answer 1

`y=(x-2)^2+(-7)` with vertex at `(2,-7)`

Explanation:

General vertex form:
`color(white)("XXX")y=(x-a)^2+b` with vertex at `(a,b)`

Given:
`color(white)("XXX")y=x^2-4x-3`
Complete the square:
`color(white)("XXX")y=x^2-4xcolor(green)(+4)-3color(green)(-4)`

`color(white)("XXX")y=(x-2)^2-7`

`color(white)("XXX")y=(x-2)^2+(-7)`