1. Copyright © 2011 Pearson, Inc. 6.3 Parametric Equations and Motion

2. Copyright © 2011 Pearson, Inc. Slide 6.3 - 2 What you’ll learn about Parametric Equations Parametric Curves Eliminating the Parameter Lines and Line Segments Simulating Motion with a Grapher … and why These topics can be used to model the path of an object such as a baseball or golf ball.

3. Copyright © 2011 Pearson, Inc. Slide 6.3 - 3 Parametric Curve, Parametric Equations The graph of the ordered pairs (x,y) where x = f(t) and y = g(t) are functions defined on an interval I of t-values is a parametric curve. The equations are parametric equations for the curve, the variable t is a parameter, and I is the parameter interval.

4. Copyright © 2011 Pearson, Inc. Slide 6.3 - 4 Example Graphing Parametric Equations

5. Copyright © 2011 Pearson, Inc. Slide 6.3 - 5 Example Graphing Parametric Equations

6. Copyright © 2011 Pearson, Inc. Slide 6.3 - 6 Example Eliminating the Parameter

7. Copyright © 2011 Pearson, Inc. Slide 6.3 - 7 Example Eliminating the Parameter

8. Copyright © 2011 Pearson, Inc. Slide 6.3 - 8 Example Eliminating the Parameter

9. Copyright © 2011 Pearson, Inc. Slide 6.3 - 9 Example Eliminating the Parameter

10. Copyright © 2011 Pearson, Inc. Slide 6.3 - 10 Example Eliminating the Parameter

11. Copyright © 2011 Pearson, Inc. Slide 6.3 - 11 Example Eliminating the Parameter

12. Copyright © 2011 Pearson, Inc. Slide 6.3 - 12 Example Eliminating the Parameter

13. Copyright © 2011 Pearson, Inc. Slide 6.3 - 13 Example Finding Parametric Equations for a Line

14. Copyright © 2011 Pearson, Inc. Slide 6.3 - 14 Example Finding Parametric Equations for a Line

15. Copyright © 2011 Pearson, Inc. Slide 6.3 - 15 Quick Review

16. Copyright © 2011 Pearson, Inc. Slide 6.3 - 16 Quick Review Solutions

17. Copyright © 2011 Pearson, Inc. Slide 6.3 - 17 Quick Review Solutions