# Question #648a4

Jan 26, 2017

The coordinates of the vertex are $\left(1 , - 8\right)$.

#### Explanation:

For a parabola written in the form $y = a {x}^{2} + b x + c$, we have the formula $x = \frac{- b}{2 a}$ to find the $x$ value of the vertex.

In this case $a = 1$ and $b = - 2$, so $x = \frac{- \left(- 2\right)}{2 \left(1\right)}$ = $\frac{2}{2}$ = 1

Since we know that the $x$ value of the vertex point is 1, we can substitute that back into the initial equation to find the $y$ value of this point:

$y = {\left(1\right)}^{2} - 2 \left(1\right) - 7 = - 8$

Over all, then, the coordinates of the vertex are $\left(1 , - 8\right)$.