Answer
See the graph
![](https://gradesaver.s3.amazonaws.com/uploads/solution/b0a05fa6-79db-47c9-a7fd-16abbd1c4289/result_image/1595162051.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015927Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=c2ca4a1919db3c3abbcbf58d0db1b3e9f5afd210118dbf997ebced1430a97119)
Work Step by Step
We are given:
$y=3x^2+x-5$
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 $x=\frac{-b}{2a}=\frac{-1}{2.3}=-\frac{1}{6}$
Find the y-coordinate of the vertex $y=3(-\frac{1}{6})^2+(-\frac{1}{6})-5=\frac{-61}{12}$
Hence, the vertex is $(-\frac{1}{6},\frac{-61}{12})$.