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Solving a Quadratic Equation

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Plane Curves Parametric Equations

142 Notes – Section 8.6 Plane Curves, Parametric Equations.

1. Algebra Review: Completing the Square

2. Graphing a Parabola with vertex at (h ,k ).

3. Graphing an Ellipse with center at (h ,k ).

4. Graphing a Hyperbola with center at (0 ,0 ).

Horizontal Hyperbola	Vertical Hyperbola

Equations for right/left branches	Equations for upper/lower branches

Ex) Graph: 4 x² -y² =4

5. Plane Curves.

Plane Curve:

Parametric Equations:

Ex) Graph the plane curve, C, where = 1−2t , y= 1+ t, on the
interval [−1,4].

Ex) Find an equivalent rectangular equation for the plane curve above.

Describe Orientation:

Ex) Find equivalent rectangular equation, sketch C, indicate orientation.