Answer
Zeros: $x=6$ and $x=2$
Vertex: $(4,12)$
Work Step by Step
The function can be written in factored form as follows.
$$
\begin{aligned}
y & =-3 x^2+24 x-36 \\
& =-3\left(x^2-8 x+12\right) \\
& =-3(x-6)(x-2)
\end{aligned}
$$
Therefore, the zeros are at $x=6$ and $x=2$.The axis of symmetry is midway between the zeros, so its equation is $x =\frac{6+2}{2}= 4$.
substituting $x=4$ into $y$ gives $y=-3(-2)(2)=12 $.
The vertex is $(4,12)$.
