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

##### 1 Answer
Jun 28, 2018

$y = - 2 {\left({x}^{2} - \frac{1}{2}\right)}^{2} - \frac{3}{2}$

#### Explanation:

Complete the square:
$y = - 2 {x}^{2} + 2 x - 2$
$y = - 2 \left({x}^{2} - x\right) - 2$
$y = - 2 \left({x}^{2} - x + \frac{1}{4} - \frac{1}{4}\right) - 2$
$y = - 2 {\left({x}^{2} - \frac{1}{2}\right)}^{2} + \frac{1}{2} - 2$
$y = - 2 {\left({x}^{2} - \frac{1}{2}\right)}^{2} - \frac{3}{2}$

...which is the equation in vertex form.