Use the graph of f (x) to estimate the following. a.For what x values is this curve increasing? Decreasing? Write your answer using inequalities. b.Vertex

1

Use the graph of f (x) to estimate the following.

a. For what x values is this curve increasing? Decreasing? Write your answer using inequalities.

b. Vertex

c. x-intercept(s)

4.1-1

2

Use the graph of f (x) to estimate the following.

d. y-intercept

e. f (3) = ?

f. What x value(s) will make

4.1-1

( ) 10f x

3

Use the graph of to estimate the following.

a. For what x values is this curve increasing? Decreasing? Write your answer as inequalities.

b. Vertex

c. x-intercept(s)

4.1-2

4

Use the graph of to estimate the following.

d. y-intercept

e. f (7) = ?

f. What x value(s) willmake

4.1-2

( ) 3f x

5

Use the table to estimate the vertical and horizontal intercept(s).

4.1-3

InputOutput

32

12

0

1 0

3

5 0

7 12

31

5

4

6

Create scatterplots for the following sets of data. Determine what type of model would best fit the data. If a quadratic function would be a good fit, give an estimate for the vertex and determine whether it is a maximum or minimum point.

a.

4.1-4

x y

1

3

5 22

532

18

182627

2

7


b.

4.1-4

x y

44

2 59

4 59

5 56

7 44

10 11

1

8


c.

4.1-4

x y

14.25

1 7.75

4

5

9

12

1

25.2518.2525

9

Sketch the graph of

4.2-1

2( ) 1.5( 4) 3f x x

10

Sketch the graph of

4.2-2

2( ) 0.1( 3) 5f x x

11

Sketch the graph of

4.2-3

2( ) 4 8f x x

12

The number of applicants for asylum in the United Kingdom in thousands can be modeled by where A(t) represents the number of applicants for asylum in thousands t years since 1990. Source: model derived from data found at www.homeoffice.gov.uk

a. How many applicants filed for asylum in the UK in 2003?

4.2-4

2( ) 3.5( 11) 81A t t

13


b. Sketch a graph of this model.

4.2-4

2( ) 3.5( 11) 81A t t

14


c. In what year did the number of asylum applications reach its highest?

d. Use the graph to estimate in what year(s) the number of applications was 25,000.

e. Give a reasonable domain and range for this model.

4.2-4

2( ) 3.5( 11) 81A t t

15

Give the domain and range for the following functions.

a.

b.

4.2-5

2( ) 1.5( 4) 3f x x

2( ) 0.1( 3) 5f x x

16

The average monthly high temperature in Charlotte, North Carolina, is given in the table. Source: Weatherbase.com

a. Find an equation for a model of these data.

4.3-1

Month Mar Apr May Jun Jul Aug Sep Oct Nov

Temp (°F)

62 72 80 86 89 88 82 72 62

17


b. Using your model estimate the average high temperatures during December.

4.3-1


Temp (°F)

62 72 80 86 89 88 82 72 62

2( ) 1.89( 7) 89T m m

18


c. The actual average high temperature in December for Charlotte is 53°F. How well does your model predict this value?

4.3-1


Temp (°F)

62 72 80 86 89 88 82 72 62

2( ) 1.89( 7) 89T m m

19

Graph the data and the function given on your calculator. Adjust a, h and/or k to get an eye-ball best fit.

a.

4.3-2

2( ) 4( 10) 12f x x

x y0 2885 638 01015 6317 135

12

20

Graph the data and the function given on your calculator. Adjust a, h and/or k to get an eye-ball best fit.

b.

4.3-2

x y2.85.864.2

24

2( ) 0.2( 2) 7f x x

1.26.8

8541

21

The median home value in thousands of dollars for Connecticut is given in the table. Source: www.Zillow.com

a. Find an equation for a model of these data.

4.3-3

Year 2004

2005

2006

2007

2008

Median Home value (thousands $) 267 299 307 301 279

22

The median home value in thousands of dollars for Connecticut is given in the table. Source: www.Zillow.com

b. Using your model estimate the median home value for Connecticut in 2009.

c. Give a reasonable domain and range for this model.

4.3-3

Year 2004

2005

2006

2007

2008

Median Home value (thousands $) 267 299 307 301 279

2( ) 8( 6) 307V t t

23

The amount of online retail spending in billions of dollars for groceries and pet food is given in the table. Source: Statistical Abstract 2009.

a. Find an equation for a modelof these data.

4.3-4

Year Spending (billion $)

1999 0.32000 0.42001 0.82002 1.32003 2.02004 3.02005 4.12006 5.62007 7.42008 9.12009 10.9

24

The amount of online retail spending in billions of dollars for groceries and pet food is given in the table. Source: Statistical Abstract 2009.

b. Estimate the amount spentonline for groceries and pet foodin 2011.

c. Give a reasonable domainand range for your model.

4.3-4

Year Spending (billion $)

1999 0.32000 0.42001 0.82002 1.32003 2.02004 3.02005 4.12006 5.62007 7.42008 9.12009 10.9

2( ) 0.11( 9) 0.3G t t

25

Solve

4.4-1

23 5( 3) 17x

26

In section 4.3 classroom example 3 we looked at the median home values in Connecticut and found the model

Where V(t) represents the median home value in thousands of dollars for Connecticut t years since 2000.

a. Find when the median home value was $200,000.

b. Find the horizontal intercepts and explain their meaning.

4.4-2

2( ) 8( 6) 307V t t

27

Solve the following.

a. b.

4.4-3

23 12 15x 21.5( 4) 14 82n

28

Solve the following.

c.

4.4-3

2( 5) 20 4p

29

Solve by completing the square of

4.4-4

23 24 60 0x x

30

Solve by completing the square.

a. b.

4.4-5

2 12 11 0x x 22 16 4m m

31

Solve by completing the square.

c.

4.4-5

24 50 20a a

32

Convert to vertex form.

a. b.

4.4-6

2( ) 3 30 48f x x x 2( ) 2 5 8g x x x

33

Sketch the graph of

Give the domain and range of the function.

4.4-7

2( ) 0.75( 3.5) 18.75f x x

34

Solve the following by factoring.

a. b.

4.5-1

2 3 50 38x x 23 5 28x x

35

Solve the following by factoring.

c.

4.5-1

3 210 66 28 0x x x

36

The revenue from selling handmade pottery at an art festival can be modeled by

where represents the revenue in dollars from selling p pieces of pottery at the art festival. Find the number of pieces of pottery that must be sold to have revenue of $700.

4.5-2

( ) (100 3 )R p p p

( )R p

37

Gourmet Crepes runs a stand at the local farmers markets. When chocolate crepes sell for $10 each they sell about 350 a week. From past experience they estimate that for every 50 cent increase in price, they will sell an average of 30 fewer crepes a week.

a. What will the weekly revenue be for Gourmet Crepes if they increase the price to $11?

4.5-3

38

Gourmet Crepes runs a stand at the local farmers markets. When chocolate crepes sell for $10 each they sell about 350 a week. From past experience they estimate that for every 50 cent increase in price they will sell an average of 30 fewer crepes a week.

b. Find an equation for the model of the weekly revenue if Gourmet Crepes increases the price 50 cents x times.

4.5-3

39


c. Use your model to determine the weekly revenue if they sell chocolate crepes for $12.

4.5-3

( ) (350 30 )(10 0.5 )R x x x

40


d. Use your model to determine the weekly revenue if they sell chocolate crepes for $9.

4.5-3

( ) (350 30 )(10 0.5 )R x x x

41

Use the graph to find an equation for the quadratic.

a.

4.5-4

42

Use the graph to find an equation for the quadratic.

b.

4.5-4

43

Solve the following quadratic equations. Round your answers to three decimal places.

a. b.

4.6-1

24 3 10 0x x 22 7 9h h

44

Solve the following quadratic equations. Round your answers to three decimal places.

c.

4.6-1

22.6 3.8 4.2 0x x

45

The median home value in Gainesville Florida can be modeled by where represents the median home value in thousands of dollars for Gainesville, t years since 2000. In what year was the median home value $176,000?Source: Model derived from data found at www.zillow.com

4.6-2

2( ) 6.2 84.4 102.5V t t t ( )V t

46

Solve the following equations using any method you wish.

a. b.

4.6-3

3 24 5 6 0x x x 26 15 21p

47

Solve the following equations using any method you wish.

c. d.

4.6-3

2 6 5k k 21.3 4.1 7.2 0x x

48

Use the graph or table to estimate the solutions to the systems of equations.

a.

4.6-4

49

Use the table to estimate the solutions to the systems of equations.

b.

4.6-4

50

Solve the following systems of equations.

a. b.

4.6-5

2

2 15

2 12 7

y x

y x x

2

2

0.5 3 6.5

2 10 4

y x x

y x x

51

Find the vertical intercept and vertex of the following quadratics. State if the vertex is a minimum or maximum point on the graph.

a. b.

4.7-1

2( ) 10 12f x x x 2( ) 5 30 15g a a a

52

Find the vertical intercept and vertex of the following quadratics. State if the vertex is a minimum or maximum point on the graph.

c.

4.7-1

2( ) 4( 2) 5h t t

53

Sketch the graph of the following.

a.

4.7-2

2( ) 1.5 9 7.5f x x x

54

Sketch the graph of the following.

a.

4.7-2

2( ) 0.25 3 15f x x x

55

The monthly profit for a local water park can be modeled by

where P(d) represents the monthly profit in thousands of dollars for the local water park when tickets are sold for t dollars each.

a. What is the water park’s monthly profit if it sells tickets for $12 each?

4.7-3

2( ) 0.9 31.78 144.14P d t t

56



b. How much should the water park sell tickets for if they want a monthly profit of $125,000?

4.7-3

2( ) 0.9 31.78 144.14P d t t

57



c. Find the vertex for this model and explain its meaning in regard to the water park

4.7-3

2( ) 0.9 31.78 144.14P d t t

58

Graph the following inequalities.

a.

4.7-4

2 7 8y x x

59

Graph the following inequalities.

b.

4.7-4

22 8 9y x x

Documents

Use the graph of f (x) to estimate the following. a.For what x values is this curve increasing? Decreasing? Write your answer using inequalities. b.Vertex