need attachedPart C – Modeling Using Residuals (possible 20 points)

Do the Modeling Using Residuals Activity Lab on page 244 of your textbook.

You have learned that there is more than one model for a set of data. You can look at the y-values

on the calculator to determine which model is better. When you find these differences, you are

looking at the residuals. Residuals that are closer to zero will represent the better model!

Work through the 5 steps in the activity with your graphing calculator. You should see that for this

particular problem, the quadratic model is the best.

1.

2.

3.

Part D – Quadratic Inequalities

(possible 20 points)

Do the Quadratic Inequalities Activity Lab on page 296 of your textbook.

Use your graphing calculator to work through activities 1, 2, and 3. Do only problems 1 – 15.

Activity 1:

1.

2.

Project 2

295

MTHH 039

3.

4.

5.

6.

Activity 2:

7.

8.

9.

10.

11.

Activity 3:

12.

13.

14.

15.

Project 2

296

MTHH 039

را

Activity

Lab

Modeling Using Residuals

5

Technology

FOR USE WITH LESSON 5-1

You can use more than one model for a set of data. You can

determine which is a better model by analyzing the differences

between the y-values of the data and the y-values of each model.

These differences are called residuals. The better model will have

residuals that are closer to zero.

What Y

• To grap

function

ACTIVITY

. To find

minim

quadr

. An

The calculator screen shows the graphs of a linear model and

a quadratic model for the data below. Which model better

To max

fits the data?

revenu

Participation in Backpacking or Wilderness Camp Activities

Year (1990 = 0)

1995 1997 1999 2001 2003

Millions of Participants 10.2

12.0 15.3 14.5 13.7

SOURCE: National Sporting Goods Association

Step 1 Press STAT ENTER to enter the data in L, and L2. Then use the LinReg and

QuadReg features to find linear and quadratic models.

Step 2 Enter the linear model as Y, and the quadratic model as Y2.

Step 3 To find the residuals of the linear model and store the differences in L3,

enter L2

11 ( LD STO L3 ENTER

Step 4 Find the residuals of the quadratic

model. Store the differences in L4.

Step 5 Compare the residuals in L3 and L4.

The values in L4 are closer to zero, so

the quadratic model is the better fit.

L2(6) =

VARS

–

2.

L2

IL3

10.2

12

L4

.28857

-.8543

.83143

-.2543

-.0114

-1.04

-.19

2.16

.41

-1.34

15.3

14.5

13.7

EXERCISES

For each set of data, find a linear model and a quadratic model. Which model is the

better fit? Justify your reasoning.

1.

Money Spent in the U.S. on Personal Technology

0

10

20

22

24

26

Year (0 = 1970)

Billions of Dollars

8.8

17.6 53.8

61.2 78.5 89.7

2.

Fishing Licenses Sold

25

30

Year (0 = 1970) 0 5 10 15 20

Millions Sold 31.1 34.7 35.2 35.7 36.9

37.9 37.6

3. For each of Exercises 1 and 2, state whether the situation is discrete

and describe a reasonable domain and range. Explain your responses.

244

Activity Lab Modeling Using Residuals

Activity

Lab

Quadratic Inequalities

Technology

FOR USE WITH LESSON 5-8

You can solve quadratic inequalities using graphs, tables, and algebraic methods.

Indeed, the most effective way may be a combination of methods.

1 ACTIVITY

To find which of x2 – 12 or 3x + 6 is greater, enter the two functions as

Y and Y2 in your graphing calculator, you could use the TABLE option to

compare the two functions for various values of x, as shown below.

3

Y1

88

Y2

-24

Plot1 Plot2 Plot3

Y1 EX2 – 12

Y2 E 3X + 6

Y3 =

Y4=

Y5=

Y6 =

Y7=

TABLE SETUP

TblStart=-10

ATbl=5

Indpnt: AUTO ASK

Depend: AUTO ASK

Х

-10

-5

0

5°

10

15

20

X=-10

13

-12

13

88

213

388

-9

6

21

36

51

66

1. For which values of x in the table is x2 – 12 > 3x + 6?

2. For which values of x in the table is x2 – 12 < 3x + 6?
3. Does this table tell you all values of x for which x2 - 12 < 3x + 6? Explain.
4. In the TBLSET (TABLE SETUP) menu, change TblStart to -9 and ATbl to 3.
Display the table again. Does the table with this setup give you more
information? Why?
You can compare functions more efficiently by making one side of the inequality 0.
5. Show that x2 - 12 < 3x + 6 is equivalent to x2 – 3x – 18 < 0.
6. Enter x2 – 3x – 18 as Yz in your graphing calculator. Place the
cursor on the = sign after Y1 and press ENTER .This operation turns
off the display of the equation Y1. Turn off Y2 as well, and then
display the table. You will see the screen shown at the right. For
which values of x in the table is x2 – 3x - 18
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