Answer
See the picture below.
Work Step by Step
The parent function is $f(x)=x^2$ (in red), but the graph of $g(x)=-\frac{1}{3}(x^2)$ (in blue) will be wider, as the coefficient multplies each y-value of the parent function by $\frac{1}{3}$ and will also be reflected across the x-axis because of the coefficient of $-1$.
For drawing the exact parent graph, here is the table of values:
$f(-2)= -2^2=4$
$f(-1)= -1^2=1$
$f(0)= 0^2=0$
$f(1)= 1^2=1$
$f(2)=2^2=4$
By the use of graph transformation techniques, the graph will be shrinked by a factor of $3$ and will also be reflected across the x-axis.
For drawing the exact graph of $g(x)$ here is the table of values of the given function:
$g(-2)=-\frac{1}{3}\times -2^2=-\frac{4}{3}$
$g(-1)=-\frac{1}{3}\times -1^2=-\frac{1}{3}$
$g(0)=-\frac{1}{3}\times 0^2=0$
$g(1)=-\frac{1}{3}\times 1^2=-\frac{1}{3}$
$g(2)=-\frac{1}{3}\times2^2=-\frac{4}{3}$