Answer
Vertex: $(4, -1)$
Opens downward
x-intercept: none
y-intercept: -17
Work Step by Step
$f(x)=-x^2+8x-17$
$y=-x^2+8x-17$
$y=-(x^2-8x)-17$
$y=-(x^2-8x)-17+(-8/2)^2-(-8/2)^2$
$y=-(x^2-8x)-17+(-4)^2-(-4)^2$
$y=-(x^2-8x)-17+16-16$
$y=-(x^2-8x+16)-17+16$
$y=-(x-4)^2-1$
Vertex: $(4, -1)$
Opens downward
$x=0$
$y=-(x-4)^2-1$
$y=-(0-4)^2-1$
$y=-(-4)^2-1$
$y=-16-1$
$y=-17$
Since the graph is below the x-axis and opens downward, there are no x-intercepts.
y-intercept: -17
