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Unit 4 Lecture 33Review Test 4

Review Test 4

Objectives

- To get the most out of this presentation,

complete the review test first. - Use this presentation to check your work.
- If you get a problem wrong, go back to the

appropriate section in the textbook.

State the quadratic formula.

State the quadratic formula.

The solutions of the quadratic equation,

0 ax2 bx c, are

State the formula for the x coordinate of the

vertex.

State the formula for the x coordinate of the

vertex.

The x-coordinate of the vertex for the equation y

ax2 bx c, is,

A farmer wants to enclose adjacent rectangular

fields with 1000 feet of barbed wire fencing as

indicated below. Find the equation for the area

of the fields.

A farmer wants to enclose adjacent rectangular

fields with 1000 feet of barbed wire fencing as

indicated below. Find the equation for the area

of the fields.

Let x width

1000 - 3x what is left for the length of two

sides

A farmer wants to enclose adjacent rectangular

fields with 1000 feet of barbed wire fencing as

indicated below. Find the equation for the area

of the fields.

Let x width

1000 - 3x what is left for the length of two

sides

A farmer wants to enclose adjacent rectangular

fields with 1000 feet of barbed wire fencing as

indicated below. Find the equation for the area

of the fields.

Let x width

1000 - 3x what is left for the length of two

sides

A width length

A farmer wants to enclose adjacent rectangular

fields with 1000 feet of barbed wire fencing as

indicated below. Find the equation for the area

of the fields.

Let x width

1000 - 3x what is left for the length of two

sides

A width length

A farmer wants to enclose adjacent rectangular

fields with 1000 feet of barbed wire fencing as

indicated below. Find the equation for the area

of the fields.

Let x width

1000 - 3x what is left for the length of two

sides

A width length

A farmer wants to enclose adjacent rectangular

fields with 1000 feet of barbed wire fencing as

indicated below. Find the equation for the area

of the fields.

Let x width

1000 - 3x what is left for the length of two

sides

Lighten Up Company makes light bulbs. The cost

of making x thousand light bulbs per week is C

.5x2 14 x120. The revenue from selling x

thousand light bulbs per week is R 12x - .5x2

Find the equation for Profit

Lighten Up Company makes light bulbs. The cost

of making x thousand light bulbs per week is C

.5x2 14 x120. The revenue from selling x

thousand light bulbs per week is R 12x - .5x2

Find the equation for Profit

Profit Revenue - Cost

Revenue R - .5x2 12x

Cost C .5x2 14 x 120

The equation for profit is, Profit Revenue -

Cost

Revenue R - .5x2 12x

Cost C .5x2 14 x 120

P (- .5x2 12x) (.5x2 14 x 120)

The equation for profit is, Profit Revenue -

Cost

Revenue R - .5x2 12x

Cost C .5x2 14 x 120

P (- .5x2 12x) (.5x2 14 x 120)

P - .5x2 12x -.5x2 14 x - 120

The equation for profit is, Profit Revenue -

Cost

Revenue R - .5x2 12x

Cost C .5x2 14 x 120

P (- .5x2 12x) (.5x2 14 x 120)

P - .5x2 12x -.5x2 14 x - 120

P 1x2

The equation for profit is, Profit Revenue -

Cost

Revenue R - .5x2 12x

Cost C .5x2 14 x 120

P (- .5x2 12x) (.5x2 14 x 120)

P - .5x2 12x -.5x2 14 x - 120

P 1x2 26 x

The equation for profit is, Profit Revenue -

Cost

Revenue R - .5x2 12x

Cost C .5x2 14 x 120

P (- .5x2 12x) (.5x2 14 x 120)

P - .5x2 12x -.5x2 14 x - 120

P 1x2 26 x - 120

Graph the Profit Equation

P 1x2 26 x - 120

Graph the Profit Equation

P 1x2 26 x - 120

Vertex

Graph the Profit Equation

P 1x2 26 x - 120

Vertex

Graph the Profit Equation

P 1x2 26 x - 120

Vertex

P 1(13)2 26 (13) - 120

Graph the Profit Equation

P 1x2 26 x - 120

Vertex

P 1(13)2 26 (13) - 120

P 1(169) 338 - 120

P 49

Graph the Profit Equation

P 1x2 26 x - 120

Vertex

P 1(13)2 26 (13) - 120

P 49

Vertex (13,49) x13, P 49

Graph the Profit Equation

P 1x2 26 x - 120

X-Intercepts when P 0, what is x?

Graph the Profit Equation

P 1x2 26 x - 120

X-Intercepts when P 0, what is x?

P 1x2 26 x - 120

0 1x2 26 x - 120

Graph the Profit Equation

P 1x2 26 x - 120

X-Intercepts when P 0, what is x?

P 1x2 26 x - 120

0 1x2 26 x - 120

0 1(x2 - 26 120)

Graph the Profit Equation

P 1x2 26 x - 120

X-Intercepts when P 0, what is x?

P 1x2 26 x - 120

0 1x2 26 x - 120

0 1(x2 - 26 120)

0 1(x - 20)(x 6)

Graph the Profit Equation

P 1x2 26 x - 120

X-Intercepts when P 0, what is x?

P 1x2 26 x - 120

0 1x2 26 x - 120

0 1(x2 - 26 120)

0 1(x - 20)(x 6)

0 x 6

0 x - 20 or

Graph the Profit Equation

P 1x2 26 x - 120

X-Intercepts when P 0, what is x?

0 1x2 26 x - 120

0 1(x - 20)(x 6)

0 x - 20 or

0 x 6

x 20 or

x 6

Two solutions make P 0 x 20 and x 6 items

Graph the Profit Equation

P 1x2 26 x - 120

P-Intercept when x 0, what is P?

P 1x2 26 x - 120

Graph the Profit Equation

P 1x2 26 x - 120

P-Intercept when x 0, what is P?

P 1x2 26 x - 120

P 1(0)2 26 (0) 120 - 120

Graph the Profit Equation

P 1x2 26 x - 120

P-Intercept when x 0, what is P?

P 1x2 26 x - 120

P 1(0)2 26 (0) 120 - 120

P - 120

Graph the Profit Equation

P 1x2 26 x - 120

- Because a -1, parabola opens down
- Vertex (13, 49)
- X-Intercepts (6, 0) and (20, 0)
- P-Intercept (0, -120)

P 1x2 26 x - 120

Graph

profit

100

75

50

25

3

6

9

12

15

18

-25

21

items

-50

-75

-100

P 1x2 26 x - 120

Graph

profit

100

75

(13,49)

50

25

3

6

9

12

15

18

-25

21

items

-50

-75

-100

P 1x2 26 x - 120

Graph

profit

100

75

(13,49)

50

25

(6,0)

(20,0)

3

6

9

12

15

18

-25

21

items

-50

-75

-100

P 1x2 26 x - 120

Graph

profit

100

75

(13,49)

50

25

(6,0)

(20,0)

3

6

9

12

15

18

-25

21

items

-50

-75

-100

(0,-120)

P 1x2 26 x - 120

Graph

profit

100

75

(13,49)

50

25

(6,0)

(20,0)

3

6

9

12

15

18

-25

21

items

-50

-75

-100

(0,-120)

Explain the Profit Equation in business terms

P 1x2 26 x - 120

Explain the Profit Equation in business terms

P 1x2 26 x - 120

- Vertex (13, 49) maximum profit is 49 when 13

items are sold

Explain the Profit Equation in business terms

P 1x2 26 x - 120

- Vertex (13, 49) maximum profit is 49 when 13

items are sold - X-Intercepts (6, 0) and (20, 0) breakeven

points, 0 profit is made

Explain the Profit Equation in business terms

P 1x2 26 x - 120

- Vertex (13, 49) maximum profit is 49 when 13

items are sold - X-Intercepts (6, 0) and (20, 0) breakeven

points, 0 profit is made - P-Intercept (0, -120) fixed costs or startup

costs

Herbs Company has the following profit equation

P 2x2 28 x - 50

profit

60

(7,48)

45

30

15

(2.1,0)

(11.9,0)

2

4

6

8

10

12

-15

14

items

-30

-45

(0,-50)

-60

Herbs Company need to make a profit of 30.

Graph and find where the lines intersect.

profit

60

(7,48)

45

30

15

(2.1,0)

(11.9,0)

2

4

6

8

10

12

-15

14

items

-30

-45

(0,-50)

-60

Graph the Profit Equation

P 2x2 28 x - 50

When P 30, what is x?

P 2x2 28 x - 50

Graph the Profit Equation

P 2x2 28 x - 50

When P 30, what is x?

P 2x2 28 x - 50

30 2x2 28 x - 50

Graph the Profit Equation

P 2x2 28 x - 50

When P 30, what is x?

P 2x2 28 x - 50

Subtract 30 from both sides

30 2x2 28 x - 50

Graph the Profit Equation

P 2x2 28 x - 50

When P 30, what is x?

P 2x2 28 x - 50

Subtract 30 from both sides

30 2x2 28 x - 50

0 2x2 28 x - 80

Use the Quadratic Formula to solve

0 2x2 28 x - 80

0 ax2 bx c

Use the Quadratic Formula to solve

0 2x2 28 x - 80

0 ax2 bx c

a -2

Use the Quadratic Formula to solve

0 2x2 28 x - 80

0 ax2 bx c

a -2

b 28

Use the Quadratic Formula to solve

0 2x2 28 x - 80

0 ax2 bx c

a -2

b 28

c -80

Use the Quadratic Formula to solve

0 2x2 28 x - 80

0 ax2 bx c

a -2

b 28

c -80

Use the Quadratic Formula to solve

0 2x2 28 x - 80

0 ax2 bx c

a -2

b 28

c -80

Use the Quadratic Formula to solve

0 2x2 28 x - 80

0 ax2 bx c

a -2

b 28

c -80

Use the Quadratic Formula to solve

0 2x2 28 x - 80

Use the Quadratic Formula to solve

0 2x2 28 x - 80

Use the Quadratic Formula to solve

0 2x2 28 x - 80

Use the Quadratic Formula to solve

0 2x2 28 x - 80

Two solutions to make P 30 x 4 and x 10

items

Herbs Company need to make a profit of 30.

Graph and find where the lines intersect.

profit

60

45

30

15

2

4

6

8

10

12

-15

14

items

-30

-45

-60

Herbs Company need to make a profit of 30.

Graph and find where the lines intersect.

profit

60

45

(10,30)

(4,30)

30

15

2

4

6

8

10

12

-15

14

items

-30

-45

-60

Herbs Company need to make a profit of 30.

Graph and find where the lines intersect.

profit

60

45

(10,30)

(4,30)

30

15

2

4

6

8

10

12

-15

14

items

-30

-45

-60

Simplify

5(2x2 x 1) 3(6x2 7x 2)

Simplify

5(2x2 x 1) 3(6x2 7x 2)

10x2 5x 5 18x2 21x 6

Simplify

5(2x2 x 1) 3(6x2 7x 2)

10x2 5x 5 18x2 21x 6

10x2 5x 5 18x2 21x 6

8x2

Simplify

5(2x2 x 1) 3(6x2 7x 2)

10x2 5x 5 18x2 21x 6

10x2 5x 5 18x2 21x 6

8x2 16x

Simplify

5(2x2 x 1) 3(6x2 7x 2)

10x2 5x 5 18x2 21x 6

10x2 5x 5 18x2 21x 6

8x2 16x 1

Multiply

(2x-1)(x5)

Multiply

F O I L

(2x-1)(x5)

2x2

Multiply

F O I L

(2x-1)(x5)

2x2 10x

Multiply

F O I L

(2x-1)(x5)

2x2 10x - x

Multiply

F O I L

(2x-1)(x5)

2x2 10x - x - 5

Multiply

F O I L

(2x-1)(x5)

2x2 10x - x - 5

2x2 9x - 5

Multiply

(x-3)2

Multiply

(x-3)2 (x-3)(x-3)

Multiply

(x-3)2 (x-3)(x-3)

F O I L

(x-3)(x-3)

x2

Multiply

(x-3)2 (x-3)(x-3)

F O I L

(x-3)(x-3)

x2 - 3x

Multiply

(x-3)2 (x-3)(x-3)

F O I L

(x-3)(x-3)

x2 - 3x - 3x

Multiply

(x-3)2 (x-3)(x-3)

F O I L

(x-3)(x-3)

x2 - 3x - 3x 9

Multiply

(x-3)2 (x-3)(x-3)

F O I L

(x-3)(x-3)

x2 - 3x - 3x 9

x2 - 6x 9

Factor 9x2 6x

Factor 9x2 6x

9x2 6x 3x( )

Factor 9x2 6x

9x2 6x 3x( )

9x2 6x 3x(3x 2)

Factor x2 2x 15

Factor x2 2x 15

(x )(x )

x2 2x 15

Factor x2 2x 15

(x 5)(x 3)

x2 2x 15

Solve x2 5x 60

Solve x2 5x 60

(x 3)(x 2)0

Solve x2 5x 60

(x 3)(x 2)0

x 3 0 or x 2 0

Solve x2 5x 60

(x 3)(x 2)0

x 3 0 or x 2 0

or

x -3

Solve x2 5x 60

(x 3)(x 2)0

x 3 0 or x 2 0

or

x -2

x -3

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