Question

What is the vertex form of `y=-3x^2 + 12x - 8`?

Answer 1

The vertex form of `y=-3x^2+12x-8` is `y=-3(x-2)^2+4`

Explanation:

To derive vertex form `y=a(x-h)^2+k` from general quadratic form `y=ax^2+bx+c`,
you can use completing the square

`y=-3x^2+12x-8`
`= -3 (x^2-4x+8/3)`
`= -3 (x^2-4x +(-2)^2-(-2)^2 +8/3)`
`= -3 ((x-2)^2 -4+8/3)`
`= -3 ((x-2)^2 -4/3)`
`= -3 (x-2)^2 -4`