Parametric+Functions+(BC)

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__Introduction:__
Parametric functions are used for curves that can't be defined by a single equation. They are especially useful for describing motion (kinematics) in 2 and 3 dimensions(whoever took physics will realize how useful this is).

They also make some pretty interesting graphs.

-Butterfly Curve

Parametric functions are defined in both **x** and **y** by a third term, usually **t**.

So while a common parabola may look like this:

A parametric curve will be defined as:

Curves are generally defined as:

and may have a parameter such as.

__**Example:**__


  The arrows indicate the direction of motion which is determined by comparing the graph to a table of values. The graph is sketched slightly past the end points to indicate that there are values of **t** outside of this range. If the graph does not continue slightly then it is inferred that we cannot take any value of **t** outside that range.
 * //t// || //x// ||> //y// ||
 * -2 || 2 ||> -5 ||
 * -1 || 0 ||> -3 ||
 * [[image:http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn_files/eq0011MP.gif width="27" height="24"]] [[image:http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn_files/empty.gif width="18" height="16"]][[image:http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn_files/eq0011M.gif width="17" height="16" align="baseline"]] [[image:http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn_files/empty.gif width="1" height="24" align="top"]] || [[image:http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn_files/eq0012MP.gif width="27" height="24"]] [[image:http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn_files/empty.gif width="18" height="16"]][[image:http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn_files/eq0012M.gif width="17" height="16" align="baseline"]] [[image:http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn_files/empty.gif width="1" height="24" align="top"]] ||> -2 ||
 * 0 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0.0001pt; text-align: center;">0 ||> <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0.0001pt; text-align: center;">-1 ||
 * <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0.0001pt; text-align: center;">1 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0.0001pt; text-align: center;">2 ||> <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0.0001pt; text-align: center;">1 ||

<span style="background-color: #ffffff; font-family: 'Times New Roman',serif; font-size: medium; line-height: normal; margin: 0in 0in 0.0001pt;">Works Cited:

[] [|http://en.wikipedia.org/wiki/Parametric_equation#Usefulness] [] []