# What is the vertex form of y=x^2+8x-7?

Aug 19, 2016

$y = {\left(x + 4\right)}^{2} - 23$

#### Explanation:

Given -

$y = {x}^{2} + 8 x - 7$

The vertex form of the equation is -

$y = a {\left(x - h\right)}^{2} + k$

Where

$a$ is the coefficient of ${x}^{2}$
$h$ is the $x$ coordinate of thevertex
$k$ is the $y$ coordinate of the vertex

Vertex-

$x = \frac{- b}{2 a} = \frac{- 8}{2} = - 4$

At $x = - 4$

$y = {\left(- 4\right)}^{2} + 8 \left(- 4\right) - 7$
$y = 16 - 32 - 7 = - 23$

Then-

$a = 1$
$h = - 4$
$k = - 23$

Plug in the values in the formula

$y = a {\left(x - h\right)}^{2} + k$

$y = {\left(x + 4\right)}^{2} - 23$