1. Precalculus Pre-AP SUMMER 2015

2. Defining a Function  When defining a function, we use coordinate points… ( x, y )  Typically, we use “x” to find out the value of “y”, and vice versa.

3. Defining a Function…Parametrically  Up until this point, we’ve used equations to tell us the values of x and y.  Today, we’ll examine what it would look like if x and y were defined by equations using a THIRD variable t. This is called a parameter.

4. Parametric Equations  Why…  Some functions and graphs can best be defined parametrically, rather than only using x and y.

5. Parametric Equations  Example  X and Y are defined by the equations… x = t + 1 y = t 2 + 2t Find the points determined by… t = -3, -2, -1, 0, 1, 2, and 3.

6. Parametric Equations  Example  X and Y are defined by the equations… x = t + 1 y = t 2 + 2t Find an algebraic relationship between x and y. This is often called (“eliminating the parameter”). Is this relationship a function?

7. Parametric Equations Pg. 135 # 1-8

8. Applications of Parametric Equations  Remember projectile motion from Algebra 2… y = -16t 2 + v 0 t + y 0

9. Applications of Parametric Equations  Remember projectile motion from Algebra 2… y = -16t 2 + v 0 t + y 0 This was okay, but what DIDN’T we account for with this equation?

10. Projectile Motion… Version 2.0!!!

12.  Example 1 A golf ball is hit at an angle of 65 o with an initial velocity of 71 feet per second. Write a set of parametric equations to represent this situation. What is the maximum height of the ball?

13. Projectile Motion… Version 2.0!!!  Example 1 A golf ball is hit at an angle of 65 o with an initial velocity of 71 feet per second. How long was the ball in the air? How far has the ball traveled horizontally before it hits the ground?

14. Projectile Motion… Version 2.0!!!  Example 1 A golf ball is hit at an angle of 65 o with an initial velocity of 71 feet per second. How high was the ball after 1.1 seconds?

15. Projectile Motion… Version 2.0!!!  Example 2 A rock is thrown off of a 121 meter cliff at an angle of 43 degrees. The initial velocity is 28 meters per second. Write a set of parametric equations to represent this situation. What is the maximum height of the rock?

16. Projectile Motion… Version 2.0!!!  Example 2 A rock is thrown off of a 121 meter cliff at an angle of 43 degrees. The initial velocity is 28 meters per second. How long was the rock in the air? How far did the rock travel horizontally before it hit the ground?

17. Projectile Motion… Version 2.0!!!  Example 2 A rock is thrown off of a 121 meter cliff at an angle of 43 degrees. The initial velocity is 28 meters per second. How high was the ball after 0.6 seconds?