Date Calculus AB Ms. Brewer

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Presentation transcript:

Date Calculus AB Ms. Brewer 1.4 Parametric Equations Date Calculus AB Ms. Brewer

Vocab/Formulas Relation: set of ordered pairs (x,y) of real numbers. If x and y are functions of t (the parameter), you can use parametric mode in a calculator.

Example 1: Graph the half parabola using the parametric equations. t x y Initial Point: Terminal Point: Direction in which curve is traced: Your calculator can only draw a parametric curve in a closed interval even when the curve has no endpoints!

Example 1: Find a Cartesian equation for the curve.

Vocab/Formulas Parametric Curve and Equations: If x and y are given as functions over an interval of t-values, then the set of points (x,y)=(f(t),g(t)) defined by these equations is a parametric curve. The equations are parametric equations. Parameter: t when a ≤ t ≤ b Parameter Interval

Parameterizing Circles and Ellipses

Example 2: Graph the parametric curve

Example 3: Draw and identify the graph of the parametric curve determined by:

Example 3: Confirm algebraically that this is a line.

Example 4: Graph the “Witch of Agnesi” Example 4: Graph the “Witch of Agnesi”. See the history of Maria Gaetana Agnesi on pg. 33

Example 5: Find a parameterization for the line segment with endpoints (-2,1) and (3,5)

Assignment Pg. 34 1-4, 9, 13, 17, 19, 21, 23, 25