# How do I use the vertex formula to determine the vertex of the graph for y=5-8x-x^2?

May 15, 2015

Put it in standard order:

$y = - {x}^{2} - 8 x + 5$ so we can see that $a = - 1$ and $b = - 8$

The vertex has $x$-coordinate $- \frac{b}{2 a}$. In this case we get:

The vertex has $x$-coordinate $- \frac{- 8}{2 \left(- 1\right)} = - \frac{- 8}{- 2} = - \frac{8}{2} = - 4$

Knowing the $x$-coordinate of the vertex, we use the equation to find the $y$-coordinate of the vertex:

$y = - {\left(- 4\right)}^{2} - 8 \left(- 4\right) + 5$

$y = - 16 + 32 + 5 = 16 + 5 = 21$

The vertex is $\left(- 4 , 21\right)$