Answer
Please see the graph.
Work Step by Step
$y=-.5x^2+4x+1$
vertex
$x=-b/2a$
$x=-4/2*-.5$
$x=-4/-1 = 4$
$y=-.5x^2+4x+1$
$y=-.5*4^2+4*4+1$
$y=-.5*16+16+1$
$y=-8+17$
$y=9$
$(4,9)$
One other point on the line
$x=0$
$y=-.5x^2+4x+1$
$y=-.5*0^2+4*0+1$
$y=-.5*0+0+1$
$y=0+0+1 = 1$
$(0,1)$
The vertex is labeled, and the axis of symmetry is the blue line.