The swallowtail catastrophe curves are defined by the parametric equations x = 2ct – 4t3, y = – ct2 + 3t4. Graph several of these curves. What features do the curves have in common? How do they change...

The swallowtail catastrophe curves are defined by the parametric equations x = 2ct – 4t3, y = – ct2 + 3t4. Graph several of these curves. What features do the curves have in common? How do they change when increases?