Answer
See the picture below.
Work Step by Step
By calculating the values of $f(x)=3x^2-2$ (with blue) and $g(x)=x^2$ (with red) we can see that the following equation is true: $3g(x)-2=f(x)$
In order to graph the parent function , here is the table of values:
$g(-2)=-2^2=4$
$g(-1)=-1^2=1$
$g(0)=0^2=0$
$g(1)=1^2=1$
$g(2)=2^2=4$
Therefore the graph of $f(x)$ is exactly the same as the graph of $g(x)=x^2$ but is wider (is stretched vertically by a factor of 3) and is translated 2 unit down.