Answer
See the graph
Work Step by Step
We are given:
$y=-\frac{1}{2}x^2+4x+1$
Let's list some values:
$x=-2 \rightarrow y=7$
$x=-1 \rightarrow y=\frac{9}{2}$
$x=0 \rightarrow y=1$
$x=1 \rightarrow y=\frac{9}{2}$
$x=2 \rightarrow y=7$
The x-coordinate of the vertex is given by $x=\frac{-b}{2a}=\frac{-4}{2.\frac{-1}{2}}=4$
Find the y-coordinate of the vertex: $y=-\frac{1}{2}(4)^2+4(4)+1=9$
Hence, the vertex is $(4,9)$.
