For Educational Use Only © 2010 12.1 Functions Involving Square Roots Brian Preston Algebra 1 2009-2010.

For Educational Use Only © 2010

12.1 Functions Involving Square

Roots Brian Preston

Algebra 1 2009-2010


Real World Application

What is the biggest pendulum you have seen?


Lesson Objectives1) Evaluate and graph a function involving square roots.

2) Use functions involving square roots to model real-life problems, such as the length of a cycle of a pendulum.


Graph y = 2x + 1

-1

-3

-2

-4-5

-1-3 -2-4-5

1

2

3

4

5

2 3 4 51

+2 +1

(0,1)

slope = 2

y-int = 1

1

1

Regular line

Review


-1-3-5 3 51

3

1

7

5

9

New line y = ax2 + bx + c

(0,0)

(1,1)

(2,4)

(3,9)

(-1,1)

(-2,4)

(-3,9)

y = x21

Parabola line

Review


22y= +3

x–(–2)

Center-1

-3

-1-3

1

3

5

1 3-5 5

( h ,k)

–2

– 2 2

+

Review


y= + kx – ha

Graphing a Square Root

a =The bigger a is the steeper the curved line is. The smaller a is the flatter the curve line is.

(h,k)= Starting point (Center)

k = Translates (shifts) up or down.

a + kh k

Definition


y= +k

Can you take the square root of a negative number?


Definition

x – ha

-1

-3

-2

-4-5

-1-3 -2-4-5

1

2

3

4

5

2 3 4 51

X is

neg

ativ

e

Y is negative

No


y = +k

We only use the positive

quadrants.


Definition

x – ha

2-1 6 84

4

2

8

6

-1


y = +k

Square Root

Graph.


Starting point(h,k)

Definition

x – ha


y =

Sketch the graph. Find the domain & range.

Example

2-1 6 84

4

2

8

6

-1

1) x

Not the right form


00y= +


Example

x – 0

2-1 6 84

4

2

8

6

-1

Center

(h ,k)

0

0 0

1) 1

Normal


y = +0


Example

x – 0

Domain

1)

How can you get an undefined answer or error?

1

0or – 2

No negative radicals


y = +0


Example

x – 0

Domain

x – 01)

x – 0 ≥ 0

x ≥ 0

The smallest number the radical can

become is 0.

Range


y = +0


Example

x – 0

Domain

1)

x – 0 ≥ 0

x ≥ 0

y = +0x – 00

This is the lowest y value.

Range


00y = +


Example

x – 0

Domain

1)

x – 0 ≥ 0

x ≥ 0

Range

y ≥ 0

y ≥ 0


2) The period T (in seconds) of a pendulum is the time it takes for the pendulum to swing back and forth. The period is related to the length L (in inches) of the pendulum by the

model T = 2π . Find the period

of a pendulum with a length of eight inches. Give your answer to the nearest tenth.

period

eighteight

period


82π

L

384

L

384=T


8

How long is the pendulum period?


2) 2π384

=T

2π=T 0.20…

2π=T 0.144…

0.9=T seconds



How long does it take a cycle of the pendulum to occur?

0.9 seconds


y = – 1


Example

2-1 6 84

4

2

8

6

-1

3) x

Not the right form


y= –1


Example

x – 0

2-1 6 84

4

2

8

6

-1

– 1

Center

(h , k)

0

0 – 1

3) 1

Normal


y = – 1


Example

x – 0

Domain

x – 03)

x – 0 ≥ 0

x ≥ 0


become is 0.

Range


y = – 1


Example

x – 0

Domain

3)

x – 0 ≥ 0

x ≥ 0

y = – 1x – 00


Range


y = – 1


Example

x – 0

Domain

3)

x – 0 ≥ 0

x ≥ 0

Range

y ≥ – 1

y ≥ – 1

– 1


y = + 4


Example

2-1 6 84

4

2

8

6

-1

4) x

Not the right form


44y= +


Example

x – 0

2-1 6 84

4

2

8

6

-1

Center

(h ,k)

0

0 4

4) 1

Normal


y = +4


Example

x – 0

Domain

x – 04)

x – 0 ≥ 0

x ≥ 0


become is 0.

Range


y = +4


Example

x – 0

Domain

4)

x – 0 ≥ 0

x ≥ 0

y = +4x – 00


Range


44y = +


Example

x – 0

Domain

4)

x – 0 ≥ 0

x ≥ 0

Range

y ≥ 4

y ≥ 4


00y= +


Example

x – 3

2-1 6 84

4

2

8

6

-1

Center

(h ,k)

3

3 0

5) 1

Normal


+ 3+ 3

x – 3x – 3y = +0


Example

Domain

5)

x – 3 ≥ 0

x ≥ 3


become is 0.

Range

+ 3


00y = +


Example

x – 3

Domain

5)Range

y ≥ 0

y ≥ 0

x – 3 ≥ 0

+ 3 + 3

x ≥ 3


1y= +


Example

x + 1

2-1 6 84

4

2

8

6

-1

6)

Wrong form or think the

opposite sign.


11y= +


Example

x–(–1)

2-1 6 84

4

2

8

6

-1

Center

( h ,k)

–1

– 1 1

6) 1

Normal


– 1– 1

x–(–1)x–(–1)y = +1


Example

Domain

6)

x–(–1)≥ 0

x ≥ – 1


become is 0.

Range

– 1


11y = +


Example

Domain

6)Range

y ≥ 1

y ≥ 1– 1

x–(–1)≥ 0

x ≥ – 1

– 1

x–(–1)


y = + 0


Example

2-1 6 84

4

2

8

6

-1

7) x

Not the right form

2


00y= +


Example

x – 0

2-1 6 84

4

2

8

6

-1

Center

(h , k)

0

0 0

7) 2

Steeper curved

line


y = +0


Example

x – 0

Domain

x – 07)

x – 0 ≥ 0

x ≥ 0


become is 0.

Range2


y = +0


Example

x – 0

Domain

7)

x – 0 ≥ 0

x ≥ 0

y = +0x – 00


Range2


00y = +


Example

x – 0

Domain

7)

x – 0 ≥ 0

x ≥ 0

Range

y ≥ 0

y ≥ 0

2


33y= +


Example

x – 4

2-1 6 84

4

2

8

6

-1

Center

(h ,k)

4

4 3

8) 2

Steeper curved

line


+ 4+ 4

x – 4x – 4y = +3


Example

Domain

8)


become is 0.

Range2

x – 4 ≥ 0

x ≥ 4

+ 4


33y = +


Example

Domain

8)Range

y ≥ 3

y ≥ 3

x – 42

+ 4x – 4 ≥ 0

x ≥ 4

+ 4


99y =

Evaluate the function for the given value of x.

Example

9) 3

9

x ;

y = 3 x


9

9y =


Example

9) 3 x ;

y = 3

3y = 3

y = 9


– 2– 2

x

y =


Example

10)

(– 2)

21 – 2x ;

y = 21 – 2

y = 21

y =

+ 4

= 525


x

y =


Example

11)

( )

36x – 2 ;

y = 36

y = 18

y =

– 2

= 416

– 2

1

21

2


1) Don’t forget the negative signs.

2) Make sure you have the right center.

Key Points & Don’t Forget

y= +kx – ha(h,k) not (– h,k)

h


pg. 496-497 #’s 18-42 even, 43-45, 52-64 even

The Assignment


Please email [email protected] with errors, confusing slides, improvements, complications, or any other comments or questions.

The template is from www.spiralgraphics.biz

http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.

Bibliography

For Educational Use Only © 2010 12.1 Functions Involving Square Roots Brian Preston Algebra 1 2009-2010.

Documents