Answer
See the graph
Work Step by Step
We are given: $y=-2x^2+8x+1$
$y=-2(x^2-4x)+1$
$y=-2(x-2)^2+9$
Hence here, $a=-2,h=2,k=9$
The vertex is $(2,9)$
The axis of symmetry is: $x=2$
Make a list of values:
$x=0 \rightarrow y=1$
$x=4 \rightarrow y=1$
$x=1 \rightarrow y=7$
$x=3 \rightarrow y=7$