Answer
The function has a maximum value.
The maximum value is $8$.
Work Step by Step
Comparing $y=-x^{2}+6x-1$ with $ax^{2}+bx+c$, we see that $a=-1$ and $b=6$.
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
$x=-\frac{b}{2a}=-\frac{6}{2(-1)}=3$
Evaluating the function at $x=3$, we get the y-coordinate of the vertex as
$y=-(3)^{2}+6(3)-1=8$
