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

Dec 21, 2016

The vertex form of $y = - 3 {x}^{2} + 12 x - 8$ is $y = - 3 {\left(x - 2\right)}^{2} + 4$

#### Explanation:

To derive vertex form $y = a {\left(x - h\right)}^{2} + k$ from general quadratic form $y = a {x}^{2} + b x + c$,
you can use completing the square

$y = - 3 {x}^{2} + 12 x - 8$
$= - 3 \left({x}^{2} - 4 x + \frac{8}{3}\right)$
$= - 3 \left({x}^{2} - 4 x + {\left(- 2\right)}^{2} - {\left(- 2\right)}^{2} + \frac{8}{3}\right)$
$= - 3 \left({\left(x - 2\right)}^{2} - 4 + \frac{8}{3}\right)$
$= - 3 \left({\left(x - 2\right)}^{2} - \frac{4}{3}\right)$
$= - 3 {\left(x - 2\right)}^{2} - 4$