# Where is the vertex of the graph of y = x^2 + 4x + 5 located?

May 5, 2016

Vertex $\left(- 2 , 1\right)$

#### Explanation:

Given -

$y = {x}^{2} + 4 x + 5$
Find the $x$co-ordinate of the vertex.
$x - \frac{- b}{2 a} = \frac{- 4}{2 \times 1} = \frac{- 4}{2} = - 2$
Find the $y$co-ordinate
At x=-2; y=(-2)^2+4(-2)+5
$y = 4 - 8 + 5 = 9 - 8 = 1$
Vertex $\left(- 2 , 1\right)$