Answer
Please see the graph.
Work Step by Step
The graph was created using graphing software.
$y=2x^2-8x-5$
vertex:
$x=-b/2a$
$x=-(-8)/2*2$
$x=8/4 = 2$
$y=2x^2-8x-5$
$y=2(2)^2-8(2)-5$
$y=2*4-16-5$
$y=8-16-5$
$y=-13$
The green line is the axis of symmetry, and the vertex is labeled.