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

Feb 5, 2016

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

#### Explanation:

The general vertex form is
$\textcolor{w h i t e}{\text{XXX}} y = m {\left(x - a\right)}^{2} + b$ with vertex at $\left(a , b\right)$

Given
$\textcolor{w h i t e}{\text{XXX}} y = - {x}^{2} + 2 x - 2$

$\textcolor{w h i t e}{\text{XXX}} y = \left(- 1\right) \left({x}^{2} - 2 x + 2\right)$

$\textcolor{w h i t e}{\text{XXX}} y = \left(- 1\right) \left({x}^{2} - 2 x + 1 + 1\right)$

$\textcolor{w h i t e}{\text{XXX}} y = \left(- 1\right) \left({x}^{2} - 2 x + 1\right) - 1$

$\textcolor{w h i t e}{\text{XXX}} y = \left(- 1\right) {\left(x - 1\right)}^{2} + \left(- 1\right)$

which is the vertex form with $m = \left(- 1\right) , a = 1 , \mathmr{and} b = \left(- 1\right)$
graph{-x^2+2x-2 [-3.215, 6.65, -4.532, 0.4]}