Answer
Please see the graph.
Work Step by Step
The graph was made using graphing software.
$y=\frac{1}{2}x^2+8x-20$
vertex:
$x=-b/2a$
$x = -(8)/2*(.5)$
$x = -8/1$
$x = -8$
$y=\frac{1}{2}x^2+8x-20$
$y=\frac{1}{2}*8^2+8*-8-20$
$y=.5*64-64-20$
$y=32-64-20$
$y=-52$
$(-8,-52)$
Two points on the curve:
$x=0$
$y=\frac{1}{2}*0^2+8*0-20$
$y= .5*0+0 - 20$
$y = -20$
$(0,-20)$
Since the distance from 0 to the axis of symmetry is 8 units, we also know $(8,-52)$ is on the curve.
