# What is the the vertex of y = (x -3)^2+8x-15 ?

Dec 29, 2017

The vertex is $\left(- 1 , - 7\right)$.

#### Explanation:

First expand and collect like terms:

$y = {x}^{2} - 6 x + 9 + 8 x - 15$
$y = {x}^{2} + 2 x - 6$

Now the vertex is $\left(h , k\right)$, where $h = - \frac{b}{2 a}$ and $k$ is the value of $y$ when $h$ is substituted into the function.

$h = - \frac{2}{2 \cdot 1} = - 1$

$k = {\left(- 1\right)}^{2} + 2 \left(- 1\right) - 6 = 1 - 2 - 6 = - 7$

The vertex is $\left(- 1 , - 7\right)$.