Activities for Students: Introducing Parametric Equations through Graphing Calculator Explorations

The Algebra Standard of Principles and Standards for School Mathematics (NCTM 2000) suggests that the mathematics curriculum for grades 9–12 include the use of “a variety of symbolic representations, including recursive and parametric equations, for functions and relations” (p. 296). Parametric equations are very useful for representing graphs of curves that cannot otherwise be expressed as functions that define y in terms of x . The underlying idea of working with parametric equations is to express both x and y as functions of a third variable, called the parameter. The parametric equations are those functions assigned to x and y . The variable, typically t for time, makes parametric equations practical for modeling situations involving motion of an object along a given path by providing the coordinates of positions (x, y) of the object over time.