1.

2.

Warm-Up 1/16

Assignments Questions?

C

H

Rigor:You will learn how to graph parametric equations and how to write equations in rectangular form.

Relevance:You will be able to use parametric equations to solve real world problems related to the motion

of projectiles.

7-5 Parametric Equations

The variable t is called a parameter.

The values of t trace the curve in a specific direction called the orientation.

Example 1: Sketch the curve given by each pair of parametric equations over the interval.

a. and

t x y

– 4

– 3

– 2

– 1

0

1

2

3

4

21

14

9

6

5

6

9

14

21 6

5.5

5

4.5

4

3.5

3

2.5

2

Example 1: Sketch the curve given by each pair of parametric equations over the interval.

b. and

t x y

– 8

– 6

– 4

– 2

0

2

4

6

8

21

14

9

6

5

6

9

14

21 6

5.5

5

4.5

4

3.5

3

2.5

2

Example 1:

Example 2: Write the parametric equations in rectangular form.

and

𝑦=𝑡 2+2

𝑦=(− 𝑥3 )

2

+2

𝑦=19𝑥

2

+2

Example 3: Write the parametric equations in rectangular form. then graph the equation. State domain restrictions.

and

𝑦=

1

𝑥2 +1

1𝑥2

𝑥√𝑡=1

√𝑡= 1𝑥

(√𝑡 )2=( 1𝑥 )

2

𝑡=1

𝑥2

𝑦=

1𝑥2 +

𝑥2

𝑥2

1𝑥2

𝑦=

1+𝑥2

𝑥2

1𝑥2

𝑦=1+𝑥2

1𝑦=1+𝑥2

D: x >0

𝑦=𝑥2+1

𝑦=𝑡+1𝑡

Example 5: Use the parameter to write the parametric equations that can represent . Then graph the equation, indicating the speed and orientation.

a.

𝑦=𝑥2− 4𝑦=𝑡 2− 4

𝑦=𝑡 2− 4

b.

𝑥=𝑡−1

4

𝑦=( 𝑡− 14 )

2

− 4

𝑦= 𝑡2 −2 𝑡+116

−6416

𝑦= 𝑡2 −2 𝑡−6316

𝑥=𝑡−1

4

𝑦= 𝑡2

16−𝑡8

−6316

√−1math!

7-5 Assignment: TX p469, 2-16 Even & 26-36 Even only graph 2-8 not 32

Chapter 7 Test Thursday 1/23 You will need to know formulas.

Example 4: Write the parametric equations in rectangular form. then graph the equation.

and

cos𝜃=𝑥2 sin 𝜃=

44

sin2𝜃+cos2𝜃=1

( 𝑥2 )2

+( 𝑦4 )2

=1

𝑥2

4+ 𝑦2

16=1