Math Help

Parametrics – Strategy to Plot Parametric Curves

In a Nut Shell: The “parametric representation” of the function, y = f(x), is as follows:

x = x(t) y = y(t) using the parameter, t

Frequently you are asked to represent the plot, y = y(x) in the x˗y plane.

Strategy to Develop Plot

1. Eliminate the parameter, t, in favor of expressing the function as y = y(x).

Try plotting y as a function of x .

2. Plot a few points for convenient choices of the parameter, t, starting with t = 0

or other values of t where x(t) and y(t) are easy to evaluate.

3. Test for symmetry such as replace t with ˗ t .

4. Calculate the slope of the function. i.e. dy/dx = [ dy/dt ] / [ dx/dt ]

for dx/dt ≠ 0. Examine the slope of the function at various values of t.

5. Note the direction of travel of the function as t increases.

Return to Calculus 2 Notes Involving Sequences, Infinite Series, etc