EJMT Abstract

We consider the question of characterizing the behavior of parametric curves whose components are cubic polynomials. When there is no chance of confusion, we will refer to such curves as cubic curves with the understanding that each of x(t) and y(t) are themselves cubic polynomials. We classify various types of parametric cubics using their defining coefficients. We show that this can be done in an elementary fashion accessible to students with a knowledge of Calculus. We discuss the manner in which the Maple Computer Algebra System can be used to explore this family of parametric curves.