Answer
See the graph
![](https://gradesaver.s3.amazonaws.com/uploads/solution/5db7075b-ed0e-4197-b821-9499aedb8f14/result_image/1595161909.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000506Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=092cfae2d178ed7edc3d8c14a50a2fc11bd454cbc6312c17218a7c01efe1b553)
Work Step by Step
We are given:
$y=\frac{1}{2}x^2+2x-3$
Let's list some values:
$x=-2 \rightarrow y=1$
$x=-1 \rightarrow y=\frac{-1}{2}$
$x=0 \rightarrow y=-3$
$x=1 \rightarrow y=\frac{-1}{2}$
$x=2 \rightarrow y=1$
The x-coordinate of the vertex is given by $x=\frac{-b}{2a}=\frac{-2}{2.(\frac{1}{2})}=-2$
Find the y-coordinate of the vertex $y=\frac{1}{2}(-2)^2+2(-2)-3$
Hence, the vertex is $(-2,-5)$.