The given function is
[tex]g(x)=-3x^2+24x-45[/tex]
a = -3
b= 24
c = -45
[tex]\begin{gathered} h=-\frac{b}{2a} \\ h=-\frac{24}{2(-3)} \\ h=-\frac{24}{-6} \\ h=4 \end{gathered}[/tex]
Substitute x by 4 to find k
[tex]\begin{gathered} f(4)=-3(4)^2+24(4)-45 \\ f(4)=-48+96-45 \\ f(4)=3 \\ k=3 \end{gathered}[/tex]
The function is
[tex]g(x)=-3(x-4)^2+3[/tex]
The vertex is (h, k) = (4, 3)
