Answer
Please see the graph.
Work Step by Step
The graph was created using graphing software.
$f(x) = -x^2+2x-5$
vertex
$x=-b/2a$
$x=-(2)/2(-1)$
$x = -2 /-2 = 1$
$f(-1) = -(-1)^2+2*(-1)-5$
$f(-1) = -1-2-5$
$f(-1) = -1 + -2 + -5$
$f(-1) = -8$
$(-1, -8)$
Two other points on the graph:
$x=0$
$f(0) = -0^2+2*0-5$
$f(0) = 0 + 0 -5$
$f(0) = -5$
$(0, -5)$
The difference -1 and 0 (the axis of symmetry) is 1 unit, so we also know $(1, -8)$ is also a point on the graph.
