Answer
$\left\{\begin{array}{ll}
x=3\sin t, & \\
y=9\sin^{2}t, & t\in[0,+\infty)
\end{array}\right.$
Work Step by Step
One way to keep x between $-3$ and $3$, is to define $x=3\sin t$.
($x$ moves back and forth between -3 and 3).
We want $x$ to start at 0, so we start with $t$=0 (restrict $t$ to $[0,+\infty)$ )
(If we had chosen cosine to represent $x$, $t$ would have started with $\pi/2$)
Substituting $x$,
$y=x^{2}\Rightarrow y=(3\sin t)^{2}=9\sin^{2}t$
So, we can have the following:
$\left\{\begin{array}{ll}
x=3\sin t, & \\
y=9\sin^{2}t, & t\in[0,+\infty)
\end{array}\right.$
