# What is the vertex form of y= - 3x^2 - 12x - 7 ?

Apr 17, 2017

$\text{The vertex form is } y = - 3 {\left(x + 2\right)}^{2} + 5$

#### Explanation:

$y = - 3 {x}^{2} - 12 x - 7$

$y = - 3 {x}^{2} - 12 x \textcolor{red}{- 12 + 12} - 7$

$y = - 3 {x}^{2} - 12 x - \textcolor{red}{12} + 5$

$y = - 3 \left(\textcolor{g r e e n}{{x}^{2} + 4 x + 4}\right) + 5$

$\textcolor{g r e e n}{{x}^{2} + 4 x + 4} = {\left(x + 2\right)}^{2}$

$y = - 3 {\left(x + 2\right)}^{2} + 5$