1. Learning Targets Define parametric equations Graph curves parametrically within a given parametric interval Eliminate the parameter to obtain a rectangular equation

2. Using Your Graphing Calculator

3. Function Mode vs. Parametric Mode Vocabulary Parametric Equations Parameter Parameter Interval Rectangular Equation (Cartesian Equation) An equation with only x’s and y’s. …where t is called the parameter … …and t is in the parameter interval, such as 0 ≤ t ≤ 2.

4. txy -3(-3) 2 - 2 = 73(-3) = -9 -2 0 1 2 3

5. txy -3(-3) 2 - 2 = 73(-3) = -9 -2(-2) 2 - 2 = 23(-2) = -6 (-1) 2 - 2 = -13(-1) = -3 0(0) 2 - 2 = -23(0) = 0 1(1) 2 - 2 = -13(1) = 3 2(2) 2 - 2 = 23(2) = 6 3(3) 2 - 2 = 73(3) = 9

6. Using Your Graphing Calculator

8. What is a good window for this parametric curve? Parametric Interval: Domain: Range:

9. Using Your Graphing Calculator Let’s start with Tstep = 1.

10. Using Your Graphing Calculator What is a good value for Tstep? Experiment with different values. What happens when you make the value bigger? Smaller?

11. Graph the parametric equations in our example for the following parametric intervals: -3 ≤ t ≤ 1 -2 ≤ t ≤ 3 How are these different from the parametric curve we graphed earlier?

12. Learning Targets Define parametric equations Graph curves parametrically within a given parametric interval Eliminate the parameter to obtain a rectangular equation

13. Eliminating the Parameter

14. Your Turn!

15. Learning Targets Define parametric equations Graph curves parametrically within a given parametric interval Eliminate the parameter to obtain a rectangular equation

16. Homework Page 530 #’s 1 – 25 odd, 65 For the remaining time in class, we will work on #65 from the homework assignment in small groups. See page 18 in your textbook to review the equation of a circle.

18. h2-243 k33 -3

19. #65. Parametrizing Circles