Question

x(t)=t+5, y(t)=3t^2−4, where t is on the interval [−4,0].What is the rectangular form of the parametric equations?What interval does x fall under?

Answer 1

Given

The equations are given

x(t)=t+5, y(t)=3t^2−4, where t is on the interval [−4,0].

Step-by-step explanation

To find the rectangular form of parametric equations

Substitute the value of t from x in y.

`t=x-5`

Then ,

`\begin{gathered} y=3(x-5)^2-4 \\ y=3(x^2+25-10x)-4 \\ y=3x^2+75-30x-4 \\ y=3x^2-30x+71 \end{gathered}`

Answer

The rectangular form of parametric equations is

`y=3x^2-30x+71`

The interval where x fall is

`(-\infty,\infty)`