Question

How do you find the VERTEX of a parabola `y=-3x^2+12x-9`?

Answer 1

Re-write the given equation in "vertex form" to get:
`color(white)("XXXX")`vertex at `(2,3)`

Explanation:

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

Given `y = -3x^2+12x-9`

Extract `m`
`color(white)("XXXX")` `y = (-3)(x^2-4x) -9`

Complete the square:
`color(white)("XXXX")` `y = (-3)(x^2-4x+4) - 9 +3(4)`

`color(white)("XXXX")` `y = (-3)(x-2)^2 +3`
`color(white)("XXXX")` `color(white)("XXXX")`which is the vertex form
`color(white)("XXXX")` `color(white)("XXXX")`with vertex at `(2,3)`