Answer
See the graph
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 $(-2,-5)$.
