Question

What is the vertex of `y=-x^2+4x+12`? (This replaces the same question that I accidentally deleted before my first cup of coffee).

Answer 1

The vertex of `-x^2+4x+12` is at `(2,16)`

Explanation:

By rewriting `y=-x^2+4x+12`
into "vertex form": `y=m(x-a)^2+b` (with vertex at `(a,b)`)
we can simply "read off" the vertex values.

`y=-x^2+4x+12`
`color(white)("XXXX")`extract `m`
`y=(-1)(x^2-4x-12)`
`color(white)("XXXX")`complete the square
`y=(-1)(color(blue)(x^2-4x+4) -12 -4)`
`color(white)("XXXX")`rewrite as a square plus an external term
`y=(-1)(x-2)^2 +16`

This is in vertex form with the vertex at `(2,16)`