Answer
1) $x=t; y=-2t^2+1,-\infty\lt t\lt \infty$
2) $x=\dfrac{1}{2}t; y=-\dfrac{1}{2}t^2+1,-\infty\lt t\lt \infty$
Work Step by Step
We are given the rectangular equation:
$y=-2x^2+1$
One set of parametric equations is:
$\begin{cases}
x=t\\
y=-2t^2+1
\end{cases}$
with $-\infty\lt t\lt \infty$
Another set of parametric equations is:
$\begin{cases}
x=\dfrac{1}{2}t\\
y=-\dfrac{1}{2}t^2+1
\end{cases}$
with $-\infty\lt t\lt \infty$