Answer
The function will have a maximum, and the value of the maximum is $y=9$.
Work Step by Step
The function's $A$-value is negative, so it will open downwards. Therefore, the function will have a maximum. In order to figure out the value of the
$y$-coordinate of the maximum, we should take the value of the $x$-coordinate (which is $-\frac{B}{2A}$) and plug it in for the $x$-values in the function's equation. This would result in $y=-3\times(-\frac{B}{2A})^{2}+(18)\times(-\frac{B}{2A}-5)$.
$A=-3$, and $B=18$. Substituting those values into the equation results in:
$y=-3\times(-\frac{18}{2\times-3})^{2}+(18)\times(-\frac{18}{2\times-3}-5)$
$y=-3\times(3)^{2}+(18)\times(3-5)$
$y=-3\times(9)+18\times(-2)=-27+36=9$
Therefore, the value of the maximum is $y=9$.
