Answer
See the graph
![](https://gradesaver.s3.amazonaws.com/uploads/solution/d1282547-25a6-4594-b5be-277dea3ab470/result_image/1595160767.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T022356Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=dafa2712a26ed49f6c0181689f7027e28b2b2bac0ab0d87d531e01748f70f2a8)
Work Step by Step
We are given:
$y=-x^2+1$
Let's list some values:
$x=-2 \rightarrow y=3$
$x=-1 \rightarrow y=0$
$x=0 \rightarrow y=1$
$x=1 \rightarrow y=0$
$x=2 \rightarrow y=3$
The x-coordinate of the vertex is given by $x=\frac{-b}{2a}=0$
Find the y-coordinate of the vertex $y=-0^2+1=1$
Hence, the vertex is $(0, 1)$.