Answer
See the graph
![](https://gradesaver.s3.amazonaws.com/uploads/solution/6c9b6439-e9d2-4433-bd6a-e7a1fc27eba3/result_image/1595269758.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021911Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=000a6890dc6afe952e771118facb11a87bbb1cf11f887439fc643a514f49bdba)
Work Step by Step
We are given: $y=-0.5x^2+2x+1$
Make a table of values
$x=0 \rightarrow y=1$
$x=2 \rightarrow y=3$
$x=4 \rightarrow y=1$
The vertex is $(2,3)$. It is a maximum.
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