When there is a third variable, a third parameter on which
and
depend, parametric equations can be used.
To graph parametric equations by plotting points, make a table with three columns labeled
and
Choose values for
in increasing order. Plot the last two columns for
and
See
[link] and
[link] .
When graphing a parametric curve by plotting points, note the associated
t -values and show arrows on the graph indicating the orientation of the curve. See
[link] and
[link] .
Parametric equations allow the direction or the orientation of the curve to be shown on the graph. Equations that are not functions can be graphed and used in many applications involving motion. See
[link] .
Projectile motion depends on two parametric equations:
and
Initial velocity is symbolized as
represents the initial angle of the object when thrown, and
represents the height at which the object is propelled.
Section exercises
Verbal
What are two methods used to graph parametric equations?
plotting points with the orientation arrow and a graphing calculator
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?