Y-intercept: Beginning value Where graph crosses y-axis X-intercept, Zeros, Break-even point: Where graph crosses x-axis

f(2) : X-value is 2, find the y value

f(x) = 4: y value is 4 find the x value

Increasing: The x-values where the graph is going up

Decreasing: The y-value where the graph is going down

Maximum: ( , )

Minimum: ( , )

Height of a Ball

3; The height of the ball at 0 seconds

-1 second and 3 seconds

3 feet

1 second

x < 1 second

x >1 second

(1,4)

None

Y-intercept Find Break-even point:

X-intercept

Find and interpret f(5) :

Find and interpret f(x) = 8:

Increasing:

Solve by the graph: 2x – 4 = 10

-4; She starts owing $4

2 glasses of lemonade

2 glasses of lemonade

$6; She makes 6$ with 5 glasses sold

6; She makes $8 selling 6 Glasses.

Always

Profit from Sally’s Lemonade Stand

Profi

t ($)

Number of Glasses Sold7

Initial Value: Break-even point:

Find and interpret f(2) :

Find and interpret f(x) = 40:

Increasing:

Find and interpret the maximum:

When is -4x2 – 40x – 50 = 20?

Cost of Ticket ($)Pr

ofit (

Hun

dred

’s of

Dol

lars

)

Projected Profit of Concert Based on Ticket

Price

They lose $5000 if ticket price is $0

They start making money with Ticket price of $1.50

They make ~$1800 with a Ticket price of $2

They make $4000 with a ticket price of $3.50 or $6.50

x < $5.

(5,50); Maximum profit is $5000 when ticket price is $5

At x = $2.10 and $7.8

Cost of Cab Rides

Miles

Fare

($)

Company A

A(x) = x +

5

Com

pany

B

B(x)

= 3

x +

1

After how many miles will the companies be the same?

Explain when each company is a better value.

Find and interpret the y-intercept of A(x) and what does it mean?

Find and Interpret B(2)

When is 3x + 1 = 4?

When is 3x + 1 = x + 5

2 miles

B is a better value until 2 miles. After two miles, A is a better value

$5. Company A charges $5 for 0 miles

$7 Company B charges $7 for 2 miles

1 mile2 miles

x L10 -21 02 23 44 65 8

Find and Interpret Y-intercept Find Break-even point:

X-intercept

Find and interpret f(5) :

Find and interpret f(x) = 6:

Solve by the table: 2x – 2 = 4

Write the NEXT-NOW equation

Profit of Selling Popcorn

Bags Profit

Y1=2x - 2

-2; He makes -2$ if he doesn’t sell any popcorn

1 bag of popcorn

1

8; if he sells 5 bags then he will make $8

3 bags

4; If he sells 4 bags then he will make $6

Next=Now + 2; starting at -2

D: 0< x < 13.5 R: 1 < y < 9.5

Yes; Each time has just one height.

3; The height is 3 ft after 0.5 seconds.

7.5; The height is 7.5 ft after 4.5 seconds.

6.5; The height is 6.5 ft after 8.5 seconds.

3) Find and interpret the y-intercept?________________________________3; The height is 3 ft after 0 seconds.

7) When is the graph increasing?____________________________

8) When is the graph decreasing?_____________________________

9) What is the maximum height?_____________________________

1< x < 5.5

5.5< x < 7.3 and 12< x < 13.5

9.5 ft

D: 0< x < 15 R: 0.5 < y < 44

Yes; Every time has just one height.12; The height is 12 meters after 2 seconds.

5; The height is 5 meters after 8 seconds.

8.5, 11.5; The height is 20 after 8.5 and 11.5 seconds

No solution; It never reaches 46 meters.

46 isn’t between 0.5 and 44.

12+10 = 22

The height at 3 seconds plus 10

Stair Stories Climbed by Two Climbers

A(x) =(1/2)x + 5

B(x) =x +

2

Time (minutes)

Stor

ies

1. What time will they have climbed the same amount of stories?

2. How many stories will they have climbed?

3. Find and interpret the y-intercept of person A?

4. When x+2 = 4?

6 minutes

8 stories

5 stories at 0 minutes

At 2 minutes

x 'L1-1 -100 -71 -42 -13 24 5

Find and interpret y-intercept Find and interpret Break-even point:

Find and interpret zeros

Find and interpret f(4) :

Find and interpret f(x) = -4:

Solve by the graph: 3x – 7 = 2

Profit of Selling Pompoms

# of Pompoms Profit

Y = 3x - 7

-7; She loses $7 if she doesn’t sell any.

~2.3; She makes $0 if she sells 2.3 pompoms

5; She makes 5$ for selling 4 pompoms

1; She loses 4$ for selling 1 pompom

3; she makes $2 by selling 3 pompoms

~2.3; She makes $0 if she sells 2.3 pompoms.

x y1 y20 3 11 5 3.52 7 63 9 8.54 11 115 13 13.56 15 16

Delivery Charges of 2 Companies

A(x) B(x)

A(x) = 2x + 3B(x) = 2.5x + 1

After how many miles will the companies be the same?

Explain when each company is a better value.

Find and interpret the y-intercept of A(x) and what does it mean?

Find and Interpret B(2)

When is 2x + 3 = 2.5x + 1

When is 2x + 3 = 13?

Write the NEXT-NOW equation for B(x)

4 miles;

B is better for less than 4 miles;A is better for more than 4 miles;

3; Company A charges $3 for no miles traveled

6; Company B charges $6 for 2 miles traveled

X = 4

When x is 5

Next = Now + 2.5; starting at 1

Year Millions of Cars in US1950 6 1955 7.81960 7.3 1965 10.3 1970 10.1 1975 10.8 1980 11.5 1985 15.4 1990 13.5 1995 15.5 2000 17.4 2005 16.9

1. Find and interpret f(1955)7.8 million, In 1955, there were 7.8 million cars

2. Find and interpret f(x) = 17.42000; In 2000, there were 17.4 milllion cars

3. When were there 11.5 million cars In the US?In 1980

Number of Starbucks Outlets

1. Find and interpret f(2000)~5000. In 2000, there were 5000 Starbucks

2. Find and interpret the y-interceptIn 1970 there were about 1 Starbucks

3. Find and interpret f(x) = 10000In ~2006, there were 10,000 Starbucks

Starting Value Rate Increase or Decrease

Decimal multiply by

NEXT=NOW Statement

1st 4 Numbers

$20,000 5% increase 100+5 = 105% =1.05Or 1(20,000) + .05(20,000)

Next=Now*1.05 starting at 20,00

$20,000 5 % decrease

$100 4% interest

95,000 3.5% increase

8,6,4.5,

Next = Now *1.095 starting at $1000

12,20,100/3

x 15% commission

20000, 21000, 22050, 23152.50

20000, 19000, 18050, 17147.50100,104,108.16, 112.49

1000,1095, 1199, 1312.93

100-5 = 95 = .95

100+4 = 104 =1.04

100+3.5 = 103.5= 1.0350.75

1.095

1.667

.15

25% decrease

9.5% increase

66.7% increase

8

1000

12

Next = Now *.955 starting at 20000

Next = Now *1.04 starting at 100Next = Now *1.035 starting at 95000Next = Now *.75Starting at 8

Next = Now *1.667Starting at 12

95000, 98325, 101767, 105328

6/8 = .75

20/12 = 1.67