Chapter 1, Problem 52RE

To determine

To find: The parametrization for the curve.

Answer to Problem 52RE

The possible parametrization is $x=t$ and $y=t\left(t-4\right)$ for $t\le 2$ .

Explanation of Solution

Given information:The given equation is $y=x\left(x-4\right)$ for $x\le 2$ .

Calculation:

Let $x=t$ for the parametrization of the curve.

Substitute t for x in the equation $y=x\left(x-4\right)$ .

  $y=t\left(t-4\right)$

Since the domain is $x\le 2$ , substitute in $x=t$ gives the interval $t\le 2$ for the parametrization.

Therefore, the possible parametrization is $x=t$ and $y=t\left(t-4\right)$ for $t\le 2$ .