WELCOME TO

FUNCTIONALLY FANTASTIC FUNLAND

WHERE FUN IS ALL THAT MATTERS…

Dr. Jennifer L. Bell, © 2011,LaGrange High School, LaGrange, Georgia

(MCC9 12.A.REI.4b; MCC9 12.F.IF.4;‐ ‐MCC9 12.F.IF.5; MCC9 12.F.IF.6; MCC9‐ ‐ ‐

12.F.IF.7a; MCC9 12.F.IF.8a; MCC9 12.A.CED.1; ‐ ‐MCC9 12.A.CED.2; MCC9 12.F.BF.3)‐ ‐

Today’s Special Group Rates:•A group of 20 costs $40 per person. •For every extra person, you save 50¢ per person.

(Example… a group of 21 costs $39.50 each.)•For groups below 20, it costs 50¢ more for each person below 20.

(Example… a group of 17 costs $41.50 each.)# in group Price per person Total $

0102030405060708090

100

$40 $800

$50 $0$45 $450

$35 $1050$30 $1200$25 $1250$20 $1200$15 $1050$10 $800$5 $450$0 $0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

number of people in the group

1200

1100

1000

900

800

700

600

500

400

300

200

100

Questions

1.In order to get the most money from a group, how many people should there be in a group? _____________

2.What is the maximum revenue? ______________________________What is the term for this characteristic? _________________

50

$1250

vertex

3. What happens at 0 people and 100 people? _____________________What is the term for this characteristic? ________________

4. What happens after 100 people? Does this make sense? Explain.________________________________________________________

zero revenue

x-interceptsor zeros

The Park pays each person to attend (negative

admission).

5. Write the quadratic function in vertex form. ___________________

6. Describe all transformations compared to x2. _____________________________________________

y = (x - )250 + 1250-

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

number of people in the group

1200

1100

1000

900

800

700

600

500

400

300

200

100

5. Write the quadratic function in vertex form. ___________________

6. Describe all transformations compared to x2. _____________________________________________

y = (x - )250 + 1250-½

reflection acrossthe x-axis; vertical shrink;

right 50 units; up 1250 units

• domain?

• range?

• end behavior?

• vertex?

• extrema?

• rate of change?

7. Describe all characteristics of this function.

• axis of symmetry?

• x-intercept(s)?

• y-intercept?

• interval of increasing?

• interval of decreasing?

(-∞, ∞)(-∞, 1250](50, 1250)maximum

fallingx = 50(0, 0) & (100, 0)(0, 0)

[50, ∞)(-∞, 50]