Answer
The axis of symmetry is $x=-1$.
The vertex is $(-1,8)$.
Work Step by Step
Comparing $y=-9x^{2}-18x-1$ with $y=ax^{2}+bx+c$, we see that $a=-9$ and $b=-18$.
Axis of symmetry is given by
$x=-\frac{b}{2a}=-\frac{-18}{2(-9)}=-1$
The axis of symmetry is $x=-1$.
As the axis of symmetry is $x=-1$, the x-coordinate of the vertex is $-1$.
We can use the function to find the y-coordinate.
$y=-9x^{2}-18x-1$
$=-9(-1)^{2}-18(-1)-1=8$
The vertex is $(-1,8)$.
