1. 4 minutes
Warm-Up
Complete the table by evaluating each expression for the given values of x. x
4x + 3
-6x - 5 -2 -1 1 2

2. 3.6.1 Parametric Equations Objectives:
Graph a pair of parametric equations
Write the function represented by a pair of parametric equations

3. Parametric Equations
A pair of parametric equations is a pair of continuous functions that define the x- and y-coordinates of a point in a coordinate plane in terms of a third variable, such as t, called the parameter.
Altitude (ft)
3 seconds
Horizontal distance (ft)

4. Example 1 Graph the pair of parametric equations below for t x y -3 -2-1 1 2 3
(-3) - 1
= -4
-2(-3) + 3
= 9
(-2) - 1
= -3
-2(-2) + 3
= 7
(-1) - 1
= -2
-2(-1) + 3
= 5
(0) - 1
= -1
-2(0) + 3
= 3
(1) - 1
= 0
-2(1) + 3
= 1
(2) - 1
= 1
-2(2) + 3
= -1
(3) - 1
= 2
-2(3) + 3
= -3

5. Practice
Graph the pair of parametric equations
for

6. Example 2
Write the pair of parametric equations as a single equation in x and y.
y = -2
+ 7
x(t) = 3t - 5
solve for t
x = 3t - 5
3t = x + 5

7. Practice
Write the pair of parametric equations as a single equation in x and y.

8. Homework
p.199 #9,13,15,17,21

9. 4 minutes
Warm-Up
Write the pair of parametric equations as a single equation in x and y. 1) 2)

10. 3.6.2 Parametric Equations Objectives:
Graph a pair of parametric equations, and use them to model real-world applications

11. Example 1
An outfielder throws a softball to the third baseman 290 feet away to stop a runner. The ball is released 6 feet above the ground with a horizontal speed of 75 feet per second and a vertical speed of 44 feet per second. The third baseman’s mitt is held 3 feet above the ground. The following parametric equations describe the path of the ball, where t is the number of seconds after the ball is released:
a) When does the ball reach is greatest altitude?
b) Can the third baseman catch the ball?

12. Homework
study guide