Answer
Please see the graph.
Work Step by Step
$y=-2x^2+10x-1$
Axis of symmetry: $x=-b/2a$
$x=-b/2a$
$x=-(10)/2*(-2)$
$x=-10/-4$
$x=2.5$
$y=-2x^2+10x-1$
$y=-2(5/2)^2+10(5/2)-1$
$y=-2*(25/4)+50/2-1$
$y=-25/2+50/2-1$
$y=25/2-1$
$y=23/2$
$(5/2, 23/2)$
Let $x=0$
$y=-2x^2+10x-1$
$y=-2*0^2+10*0-1$
$y=-2*0+0-1$
$y=0-1$
$y=-1$
$(0,-1)$
Since $(0,-1)$ is 5/2 units from the axis of symmetry, we also know $(5,-1)$ is 5/2 units from the axis of symmetry and on the curve.
