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

Dec 7, 2015

$y = \left(- 1\right) {\left(x - \left(- 1\right)\right)}^{2} + 4$

#### Explanation:

The vertex form of a quadratic is
$\textcolor{w h i t e}{\text{XXX")y=m(x-color(red)(a))^2+color(blue)(b)color(white)("XXX}}$with vertex at $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$

Given $y = - {x}^{2} - 2 x + 3$

Extract the $m$ factor from the terms including an $x$
$\textcolor{w h i t e}{\text{XXX}} y = \left(- 1\right) \left({x}^{2} + 2 x\right) + 3$

Complete the square:
$\textcolor{w h i t e}{\text{XXX}} y = \left(- 1\right) \left({x}^{2} + 2 x + 1 - 1\right) + 3$

$\textcolor{w h i t e}{\text{XXX}} y = \left(- 1\right) \left({x}^{2} + 2 x + 1\right) + 1 + 3$

$\textcolor{w h i t e}{\text{XXX}} y = \left(- 1\right) {\left(x + 1\right)}^{2} + 4$

$\textcolor{w h i t e}{\text{XXX}} y = \left(- 1\right) {\left(x - \left(\textcolor{red}{- 1}\right)\right)}^{2} + \textcolor{b l u e}{4}$
which is the graph{-x^2-2x+3 [-6.737, 5.753, -0.565, 5.675]} vertex form with vertex at $\left(\textcolor{red}{- 1} , \textcolor{b l u e}{4}\right)$