PARAMETRIC FUNCTIONS Section 10 6 A Precalculus Pre

PARAMETRIC FUNCTIONS Section 10. 6 A Precalculus Pre. AP/Dual, Revised © 2017 viet. dang@humbleisd. net 1/18/2022 9: 58 AM § 10. 6 A: Parametric Functions 1

DEFINITIONS 1/18/2022 9: 58 AM § 10. 6 A: Parametric Functions 2

PARAMETRIC CURVES 1/18/2022 9: 58 AM § 10. 6 A: Parametric Functions 3

VISUAL EXAMPLE 1/18/2022 9: 58 AM § 10. 6 A: Parametric Functions 4

PARAMETRIC APPLICATIONS OF PROJECTILE SIMULATION 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 5

GRAPHING CALCULATOR SIMULATION 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 6

GRAPHING CALCULATOR SIMULATION 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 7

GRAPHING CALCULATOR SIMULATION 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 8

STEPS 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 9

EXAMPLE 1 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 10

EXAMPLE 1 (CALC. ) 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 11

EXAMPLE 2 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 12

EXAMPLE 2 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 13

YOUR TURN 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 14

ELIMINATE THE PARAMETER 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 15

IN GENERAL… 1/18/2022 9: 59 AM § 10. 6 A: Parametric Functions 16

EXAMPLE 3 1/18/2022 10: 00 AM § 10. 6 A: Parametric Functions 17

EXAMPLE 3 – 1 0 3 1/18/2022 10: 00 AM Und. § 10. 6 A: Parametric Functions 18

YOUR TURN 1/18/2022 10: 00 AM § 10. 6 A: Parametric Functions 19

EXAMPLE 4 1/18/2022 10: 00 AM § 10. 6 A: Parametric Functions 20

EXAMPLE 4 1/18/2022 10: 00 AM § 10. 6 A: Parametric Functions 21

EXAMPLE 4 1/18/2022 10: 00 AM § 10. 6 A: Parametric Functions 22

EXAMPLE 5 1/18/2022 10: 00 AM § 10. 6 A: Parametric Functions 23

YOUR TURN 1/18/2022 10: 00 AM § 10. 6 A: Parametric Functions 24

PROJECTILE MOTION 1/18/2022 10: 01 AM § 10. 6 A: Parametric Functions 25

EXAMPLE 6 1/18/2022 10: 01 AM § 10. 6 A: Parametric Functions 26

EXAMPLE 6 A 1/18/2022 10: 01 AM § 10. 6 A: Parametric Functions 27

EXAMPLE 6 B 1/18/2022 10: 01 AM § 10. 6 A: Parametric Functions 28

YOUR TURN Suppose that Joe hit a golf ball with an initial velocity of 150 feet per second at an angle of 30 degrees to the horizontal. (a) Find parametric equations that describe the position of the ball as a function of time. (b) How long is the golf ball in the air? (c) Determine the distance that the ball traveled. 1/18/2022 10: 01 AM § 10. 6 A: Parametric Functions 29

YOUR TURN Suppose that Joe hit a golf ball with an initial velocity of 150 feet per second at an angle of 30 degrees to the horizontal. (a) Find parametric equations that describe the position of the ball as a function of time. 1/18/2022 10: 01 AM § 10. 6 A: Parametric Functions 30

YOUR TURN Suppose that Joe hit a golf ball with an initial velocity of 150 feet per second at an angle of 30 degrees to the horizontal. (b) How long is the golf ball in the air? 1/18/2022 10: 01 AM § 10. 6 A: Parametric Functions 31

YOUR TURN Suppose that Joe hit a golf ball with an initial velocity of 150 feet per second at an angle of 30 degrees to the horizontal. (c) Determine the distance that the ball traveled. 1/18/2022 10: 01 AM § 10. 6 A: Parametric Functions 32

ASSIGNMENT Worksheet 1/18/2022 10: 01 AM § 10. 6 A: Parametric Functions 33