1. Graphing with Parametric Equations

I was looking at a chapter in my calculus book on parametric equations and I found the following exercise.

Graph:
$x=y-3y^3+y^5$

Usually I would just use the standard methods of calculus to graph the function $y=x-3x^3+x^5$, and then I would flip it over.

However, since it is in the chapeter on parametric equations, I figured there may be a clever way to parameterize this and graph it. However, I'm not seeing it.

I was looking at a chapter in my calculus book on parametric equations and I found the following exercise.

Graph:
$x=y-3y^3+y^5$

Usually I would just use the standard methods of calculus to graph the function $y=x-3x^3+x^5$, and then I would flip it over.

However, since it is in the chapeter on parametric equations, I figured there may be a clever way to parameterize this and graph it. However, I'm not seeing it.
$x = t - 3t^2 + t^5$

$y = t$

3. Originally Posted by skeeter
$x = t - 3t^2 + t^5$

$y = t$
I definitely noticed that one. But the parametric equations $x=t-3t^3+t^5$, $y=t$ don't make the shape of the curve any more obvious than $x=y-3y^3+y^5$. I was speculating that there may be a parametrization that would allow me to easily graph
y(t) and x(t) and then draw the curve based on those graphs. Otherwise, it would be pointless to parameterize at all.

4. I don't believe there is a magic bullet for an easy parametric in this case.

If someone can come up with one, they'll be sure to point it out.