Answer
The function has a maximum value.
The maximum value is 12.
Work Step by Step
Comparing $f(x)=-5x^{2}+10x+7$ with $ax^{2}+bx+c$, we see that $a=-5$ and $b=10$.
As $a\lt0$, the parabola opens down and the function has a maximum value. The maximum value is the y-coordinate of the vertex.
The x-coordinate of the vertex is given by
$x=-\frac{b}{2a}=-\frac{10}{2(-5)}=1$
Evaluating the function at $x=1$, we get the y-coordinate of the vertex as
$f(1)=-5(1)^{2}+10(1)+7=12$
