Answer
See below.
Work Step by Step
Let's compare $f(x)=-2x^2+12x+3$ to $f(x)=ax^2+bx+c$. We can see that a=-2, b=12, c=3. $a\lt0$, hence the graph opens down, hence its vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{12}{2\cdot(-2)}=3.$ Hence the maximum value is $f(3)=-2(3)^2+12(3)+3=-18+36+3=21.$
