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## Unit 4 Lecture 33 Review Test 4

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### Unit 4 Lecture 33 Review Test 4 Review Test #4 Objectives To get the most out of this presentation, complete the review test first. Use this presentation to check ... – PowerPoint PPT presentation

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Title: Unit 4 Lecture 33 Review Test 4

1
Unit 4 Lecture 33Review Test 4
Review Test 4
2
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.

3
4
The solutions of the quadratic equation,
0 ax2 bx c, are
5
State the formula for the x coordinate of the
vertex.
6
State the formula for the x coordinate of the
vertex.
The x-coordinate of the vertex for the equation y
ax2 bx c, is,
7
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.
8
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
9
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
10
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
11
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
12
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
13
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
14
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
15
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
16
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)
17
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
18
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
19
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
20
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
21
Graph the Profit Equation
P 1x2 26 x - 120
22
Graph the Profit Equation
P 1x2 26 x - 120
Vertex
23
Graph the Profit Equation
P 1x2 26 x - 120
Vertex
24
Graph the Profit Equation
P 1x2 26 x - 120
Vertex
P 1(13)2 26 (13) - 120
25
Graph the Profit Equation
P 1x2 26 x - 120
Vertex
P 1(13)2 26 (13) - 120
P 1(169) 338 - 120
P 49
26
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
27
Graph the Profit Equation
P 1x2 26 x - 120
X-Intercepts when P 0, what is x?
28
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
29
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)
30
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)
31
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
32
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
33
Graph the Profit Equation
P 1x2 26 x - 120
P-Intercept when x 0, what is P?
P 1x2 26 x - 120
34
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
35
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
36
Graph the Profit Equation
P 1x2 26 x - 120
1. Because a -1, parabola opens down
2. Vertex (13, 49)
3. X-Intercepts (6, 0) and (20, 0)
4. P-Intercept (0, -120)

37
P 1x2 26 x - 120
Graph
profit
100
75
50
25
3
6
9
12
15
18
-25
21
items
-50
-75
-100
38
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
39
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
40
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)
41
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)
42
Explain the Profit Equation in business terms
P 1x2 26 x - 120
43
Explain the Profit Equation in business terms
P 1x2 26 x - 120
1. Vertex (13, 49) maximum profit is 49 when 13
items are sold

44
Explain the Profit Equation in business terms
P 1x2 26 x - 120
1. Vertex (13, 49) maximum profit is 49 when 13
items are sold
2. X-Intercepts (6, 0) and (20, 0) breakeven

45
Explain the Profit Equation in business terms
P 1x2 26 x - 120
1. Vertex (13, 49) maximum profit is 49 when 13
items are sold
2. X-Intercepts (6, 0) and (20, 0) breakeven
3. P-Intercept (0, -120) fixed costs or startup
costs

46
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
47
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
48
Graph the Profit Equation
P 2x2 28 x - 50
When P 30, what is x?
P 2x2 28 x - 50
49
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
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
51
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
52
Use the Quadratic Formula to solve
0 2x2 28 x - 80
0 ax2 bx c
53
Use the Quadratic Formula to solve
0 2x2 28 x - 80
0 ax2 bx c
a -2
54
Use the Quadratic Formula to solve
0 2x2 28 x - 80
0 ax2 bx c
a -2
b 28
55
Use the Quadratic Formula to solve
0 2x2 28 x - 80
0 ax2 bx c
a -2
b 28
c -80
56
Use the Quadratic Formula to solve
0 2x2 28 x - 80
0 ax2 bx c
a -2
b 28
c -80
57
Use the Quadratic Formula to solve
0 2x2 28 x - 80
0 ax2 bx c
a -2
b 28
c -80
58
Use the Quadratic Formula to solve
0 2x2 28 x - 80
0 ax2 bx c
a -2
b 28
c -80
59
Use the Quadratic Formula to solve
0 2x2 28 x - 80
60
Use the Quadratic Formula to solve
0 2x2 28 x - 80
61
Use the Quadratic Formula to solve
0 2x2 28 x - 80
62
Use the Quadratic Formula to solve
0 2x2 28 x - 80
Two solutions to make P 30 x 4 and x 10
items
63
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
64
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
65
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
66
Simplify
5(2x2 x 1) 3(6x2 7x 2)
67
Simplify
5(2x2 x 1) 3(6x2 7x 2)
10x2 5x 5 18x2 21x 6
68
Simplify
5(2x2 x 1) 3(6x2 7x 2)
10x2 5x 5 18x2 21x 6
10x2 5x 5 18x2 21x 6
8x2
69
Simplify
5(2x2 x 1) 3(6x2 7x 2)
10x2 5x 5 18x2 21x 6
10x2 5x 5 18x2 21x 6
8x2 16x
70
Simplify
5(2x2 x 1) 3(6x2 7x 2)
10x2 5x 5 18x2 21x 6
10x2 5x 5 18x2 21x 6
8x2 16x 1
71
Multiply
(2x-1)(x5)
72
Multiply
F O I L
(2x-1)(x5)
2x2
73
Multiply
F O I L
(2x-1)(x5)
2x2 10x
74
Multiply
F O I L
(2x-1)(x5)
2x2 10x - x
75
Multiply
F O I L
(2x-1)(x5)
2x2 10x - x - 5
76
Multiply
F O I L
(2x-1)(x5)
2x2 10x - x - 5
2x2 9x - 5
77
Multiply
(x-3)2
78
Multiply
(x-3)2 (x-3)(x-3)
79
Multiply
(x-3)2 (x-3)(x-3)
F O I L
(x-3)(x-3)
x2
80
Multiply
(x-3)2 (x-3)(x-3)
F O I L
(x-3)(x-3)
x2 - 3x
81
Multiply
(x-3)2 (x-3)(x-3)
F O I L
(x-3)(x-3)
x2 - 3x - 3x
82
Multiply
(x-3)2 (x-3)(x-3)
F O I L
(x-3)(x-3)
x2 - 3x - 3x 9
83
Multiply
(x-3)2 (x-3)(x-3)
F O I L
(x-3)(x-3)
x2 - 3x - 3x 9
x2 - 6x 9
84
Factor 9x2 6x
85
Factor 9x2 6x
9x2 6x 3x( )
86
Factor 9x2 6x
9x2 6x 3x( )
9x2 6x 3x(3x 2)
87
Factor x2 2x 15
88
Factor x2 2x 15
(x )(x )
x2 2x 15
89
Factor x2 2x 15
(x 5)(x 3)
x2 2x 15
90
Solve x2 5x 60
91
Solve x2 5x 60
(x 3)(x 2)0
92
Solve x2 5x 60
(x 3)(x 2)0
x 3 0 or x 2 0
93
Solve x2 5x 60
(x 3)(x 2)0
x 3 0 or x 2 0
or
x -3
94
Solve x2 5x 60
(x 3)(x 2)0
x 3 0 or x 2 0
or
x -2
x -3
95
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