# What is the vertex form of y=(-x-2)(x+5)?

Nov 28, 2017

$y = - {\left(x + \frac{7}{2}\right)}^{2} + \frac{9}{4}$

#### Explanation:

$y = - {x}^{2} - 5 x - 2 x - 10$
$y = - {x}^{2} - 7 x - 10$
To make it look more 'pretty': $y = - \left({x}^{2} + 7 x + 10\right)$
Now we need to make it into Vertex Form!
$y = - {\left(x + \frac{7}{2}\right)}^{2} + \frac{9}{4}$
Let's check by solving it.
$y = - {\left(x + \frac{7}{2}\right)}^{2} + \frac{9}{4}$ =
$- \left({x}^{2} + 7 x + \frac{49}{4}\right) + \frac{9}{4}$ =
$- {x}^{2} - 7 x - \frac{49}{4} + \frac{9}{4}$ =
$- {x}^{2} - 7 x - 10$
That gets us back to our question. Therefore, we are correct!

YAY!