# What is the vertex of  y= (x+8)^2-2x-6?

Aug 18, 2017

See the solution below

#### Explanation:

$y = {x}^{2} + 16 x + 64 - 2 x - 6$
$y = {x}^{2} + 14 x + 58$

Since the equation is quadratic, Its graph would be a parabola.
graph{x^2 + 14x + 58 [-42.17, 37.83, -15.52, 24.48]}

As you can see from the graph that the roots are complex for this quadratic equation.

The vertex can be found out by the following formula,
$\left(x , y\right) = \left(- \frac{b}{2 a} , - \frac{D}{4 a}\right)$

where,
$D =$ discriminant

Also
$D = {b}^{2} - 4 a c$

here,
$b = 14$
$c = 58$
$a = 1$

Plugging in the values

$D = 196 - 4 \left(58\right) \left(1\right)$
$D = 196 - 232$
$D = - 36$

Therefore the vertex is given by
$\left(x , y\right) = \left(- \frac{14}{2} , \frac{36}{4}\right)$
$\left(x , y\right) = \left(- 7 , 9\right)$