# What is the vertex form of y= (x+2)(x - 7) ?

Jun 14, 2017

minimum vertex $- \frac{81}{4}$ at $\left(\frac{5}{2} , - \frac{81}{4}\right)$

#### Explanation:

$y = \left(x + 2\right) \left(x - 7\right) = {x}^{2} - 5 x - 14$

use completing a square to solve
$y = {x}^{2} - 5 x - 14$

$y = {\left(x - \frac{5}{2}\right)}^{2} - {\left(- \frac{5}{2}\right)}^{2} - 14$

$y = {\left(x - \frac{5}{2}\right)}^{2} - \frac{25}{4} - \frac{56}{4}$

$y = {\left(x - \frac{5}{2}\right)}^{2} - \frac{81}{4}$

since ${\left(x - \frac{5}{2}\right)}^{2}$ is +ve value, therefore it has a minimum vertex $- \frac{81}{4}$ at $\left(\frac{5}{2} , - \frac{81}{4}\right)$