Answer
Please see the graph.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/92817671-47b2-4fc4-bbeb-a1c91d56d968/result_image/1534826093.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001110Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=fd01b6231e6cc3bf740a77eb07c57e6afa1546fec6d65411eb7e4a8a94070c17)
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.