Answer
See the graph
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 $(-\frac{1}{6},\frac{-61}{12})$.
