# What is the vertex form of y= 5x^2 + 22x + 8 ?

May 29, 2017

$\text{the vertex form of equation is } y = 5 {\left(x + 2.2\right)}^{2} - 16.2$

#### Explanation:

$y = 5 {x}^{2} + 22 x + 8$

$\text{The vertex form is can be written as } y = a {\left(x - h\right)}^{2} - k$

$\text{where (h,k) is vertex coordinates}$

$y = 5 {x}^{2} + 22 x + \textcolor{red}{24.2 - 24.2} + 8$

$y = 5 {x}^{2} + 22 x + 24.2 - 16.2$

$y = 5 \left(\textcolor{g r e e n}{{x}^{2} + 4.4 x + 4.84}\right) - 16.2$

$\textcolor{g r e e n}{{x}^{2} + 4.4 x + 4.84} = {\left(x + 2.2\right)}^{2}$

$y = 5 {\left(x + 2.2\right)}^{2} - 16.2$