Chapter 10.7, Problem 30AYU

To determine

To find: Two different parametric equations for the rectangular equation.

Answer to Problem 30AYU

$x=t,y=-2t^2+1$;

$x=t-1,y=-2t^2+4t-1$

Explanation of Solution

Given:

$y=-2x^2+1$

Calculation:

Let $x=t$,

$y=-2t^2+1$

Let $x=t-1$

$y=-2{\left(t-1\right)}^2+1$

$y=-2\left(t^2+1-2t\right)+1$

$y=-2t^2-2+4t\text{ + 1}$

$y=-2t^2+4t-1$