Question

Find two different parametric equations for each rectangular equation.

$y=-2x^2+1.$

Short answer

The two different equations are-

$y=-2t^2+1y=-2t^6+1.$

Step-by-step solution

Step 1. Given information.

$y=-2x^2+1$is given.

Step 2. Calculation.

For the first parametric equation-

Let $x=t$

$$\begin{gathered} y=-2x^2+1 \\ y=-2t^2+1 \end{gathered}$$

For the second parametric equation-

Let $x=t^3$

role="math" localid="1648639076147" $$\begin{gathered} y=-2x^2+1 \\ y=-2{\left(t^3\right)}^2+1 \\ y=-2t^6+1 \end{gathered}$$