Answer
Please see the graph.
Work Step by Step
$y=.5x^2+2x-3$
vertex:
$x=-b/2a$
$x=-(2)/2(.5)$
$x=-2/1 = -2$
$y=.5x^2+2x-3$
$y=.5*(-2)^2+2*(-2)-3$
$y=.5*4+(-4)-3$
$y=2-4-3$
$y=-5$
$(-2, -5)$
One other point on the curve:
$x=0$
$y=.5x^2+2x-3$
$y=.5(0)^2+2*0-3$
$y=.5*0+0-3$
$y=0-3 = -3$
$(0,-3)$
The blue line is the axis of symmetry, and the vertex is labeled.