Answer
The axis of symmetry is $x=6$.
The vertex is $(6,9)$.
Work Step by Step
Comparing $y=-\frac{3}{4}x^{2}+9x-18$ with $y=ax^{2}+bx+c$, we see that $a=-\frac{3}{4}$ and $b=9$.
Axis of symmetry is given by
$x=-\frac{b}{2a}=-\frac{9}{2(-\frac{3}{4})}=6$
The axis of symmetry is $x=6$.
As the axis of symmetry is $x=6$, the x-coordinate of the vertex is $6$.
We can use the function to find the y-coordinate.
$y=-\frac{3}{4}x^{2}+9x-18$
When $x=6$,
$y=-\frac{3}{4}(6)^{2}+9(6)-18=9$
The vertex is $(6,9)$.
