Answer
The function has a maximum value of $17$.
Work Step by Step
Let's compare $f(x)=-3x^2+12x+5$ to $f(x)=ax^2+bx+c$.
We can see that $a=-3, b=12, c=5.$ $a\lt0$,so the graph opens down which means that its vertex is a maximum.
The maximum value is at $x=-\frac{b}{2a}=-\frac{12}{2\cdot(-3)}=2.$
Thus, the maximum value is
$f(2)=-3(2)^2+12(2)+5=17$
