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MAT 171 Chapter 3 Review
The following is a brief review of Chapter 3 for Test 2 that covers Chapters 2 & 3 and Section 10.7. This does NOT cover all the material that may be on the test.
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Dr. Claude Moore, Math Instructor, CFCC
Slide 3 - 2
Active Learning Lecture SlidesFor use with Classroom Response Systems
© 2009 Pearson Education, Inc.
Chapter 3
Copyright © 2009 Pearson Education, Inc. Slide 3 - 3
Chapter 3: Quadratic Functions and Equations; Inequalities
3.1 The Complex Numbers
3.2 Quadratic Equations, Functions, Zeros, and Models
3.3 Analyzing Graphs of Quadratic Functions
3.4 Solving Rational Equations and Radical Equations
3.5 Solving Equations and Inequalities with Absolute Values
Copyright © 2009 Pearson Education, Inc. Slide 3 - 4
Express in terms of i.
a.
c.
b.
d.
4 3i
12
2 3
2 3i
2 3i
Copyright © 2009 Pearson Education, Inc. Slide 3 - 5
Express in terms of i.
a.
c.
b.
d.
4 3i
12
2 3
2 3i
2 3i
Copyright © 2009 Pearson Education, Inc. Slide 3 - 6
Simplify: (4 – 2i) – (8 + 3i).
a. –4 – 5i
c. 12 – 5i
b. –4 + i
d. –3i
Copyright © 2009 Pearson Education, Inc. Slide 3 - 7
Simplify: (4 – 2i) – (8 + 3i).
a. –4 – 5i
c. 12 – 5i
b. –4 + i
d. –3i
Copyright © 2009 Pearson Education, Inc. Slide 3 - 8
Simplify: (3 + 2i)(4 – i).
a. 14 + 5i
c. 12 – 2i
b. 10 + 5i
d. 7 + i
Copyright © 2009 Pearson Education, Inc. Slide 3 - 9
Simplify: (3 + 2i)(4 – i).
a. 14 + 5i
c. 12 – 2i
b. 10 + 5i
d. 7 + i
Copyright © 2009 Pearson Education, Inc. Slide 3 - 10
Simplify: i17.
a. i
c. i
b. 1
d. 1
Copyright © 2009 Pearson Education, Inc. Slide 3 - 11
Simplify: i17.
a. i
c. i
b. 1
d. 1
Copyright © 2009 Pearson Education, Inc. Slide 3 - 12
Simplify: i23.
a. i
c. i
b. 1
d. 1
Copyright © 2009 Pearson Education, Inc. Slide 3 - 13
Simplify: i23.
a. i
c. i
b. 1
d. 1
Copyright © 2009 Pearson Education, Inc. Slide 3 - 14
Solve: 5x2 + 17x + 6 = 0.
a.
c.
b.
d.
23,
5
5,3
2
53,
2
2,3
5
Copyright © 2009 Pearson Education, Inc. Slide 3 - 15
Solve: 5x2 + 17x + 6 = 0.
a.
c.
b.
d.
23,
5
5,3
2
53,
2
2,3
5
Copyright © 2009 Pearson Education, Inc. Slide 3 - 16
Solve: 5t2 – 2t + 6 = 0.
a.
c.
b.
d.
1 29i
1 31
5
1 5
5
i
1 29
5
i
Copyright © 2009 Pearson Education, Inc. Slide 3 - 17
Solve: 5t2 – 2t + 6 = 0.
a.
c.
b.
d.
1 29i
1 31
5
1 5
5
i
1 29
5
i
Copyright © 2009 Pearson Education, Inc. Slide 3 - 18
Solve x2 + 6x = 2 by completing the square.
a.
c.
b.
d. 3 2 7
3 2 11
3 7
3 11
Copyright © 2009 Pearson Education, Inc. Slide 3 - 19
Solve x2 + 6x = 2 by completing the square.
a.
c.
b.
d.
3 11
3 2 7
3 2 11
3 7
Copyright © 2009 Pearson Education, Inc. Slide 3 - 20
Solve x2 + 8x = 12 by completing the square.
a.
c.
b.
d.
4 2 7
2, 6
4 8 7
2
4 2 7
Copyright © 2009 Pearson Education, Inc. Slide 3 - 21
Solve x2 + 8x = 12 by completing the square.
a.
c.
b.
d.
4 2 7
2, 6
4 8 7
2
4 2 7
Copyright © 2009 Pearson Education, Inc. Slide 3 - 22
Find the zeros of f(x) = 6x2 + 13x – 15.
a.
c.
b.
d.
5,3
6
53,
6
63,
5
15
Copyright © 2009 Pearson Education, Inc. Slide 3 - 23
Find the zeros of f(x) = 6x2 + 13x – 15.
a.
c.
b.
d.
5,3
6
53,
6
63,
5
15
Copyright © 2009 Pearson Education, Inc. Slide 3 - 24
The sum of the base and height of a triangle is 56 in. Find the height for which the area is maximum.
a. h = 14 in.
c. h = 42 in.
b. h = 28 in.
d. h = 112 in.
Copyright © 2009 Pearson Education, Inc. Slide 3 - 25
The sum of the base and height of a triangle is 56 in. Find the height for which the area is maximum.
a. h = 14 in.
c. h = 42 in.
b. h = 28 in.
d. h = 112 in.
Copyright © 2009 Pearson Education, Inc. Slide 3 - 26
For the graph of the function f(x) = 3x2 – 12x + 16 find the vertex.
a. (2, 4)
c. (2, 4)
b. (2, 52)
d. (6, 4)
Copyright © 2009 Pearson Education, Inc. Slide 3 - 27
For the graph of the function f(x) = 3x2 – 12x + 16 find the vertex.
a. (2, 4)
c. (2, 4)
b. (2, 52)
d. (6, 4)
Copyright © 2009 Pearson Education, Inc. Slide 3 - 28
For the graph of the function f(x) = 4x2 – 8x – 1 find the axis of symmetry.
a. x = 2
c.
b. x = 1
d. x = 5
1
4x
Copyright © 2009 Pearson Education, Inc. Slide 3 - 29
For the graph of the function f(x) = 4x2 – 8x – 1 find the axis of symmetry.
a. x = 2
c.
b. x = 1
d. x = 5
1
4x
Copyright © 2009 Pearson Education, Inc. Slide 3 - 30
For the graph of the function f(x) = 6x2 – 6x – 3 find the axis of symmetry.
a. x = 2
c.
b.
d. x = 2
1
4x
1
2x
Copyright © 2009 Pearson Education, Inc. Slide 3 - 31
For the graph of the function f(x) = 6x2 – 6x – 3 find the axis of symmetry.
a. x = 2
c.
b.
d. x = 2
1
4x
1
2x
Copyright © 2009 Pearson Education, Inc. Slide 3 - 32
The Cotes have 30 feet of picket fence with which to enclose a flower garden. What dimensions should the garden have in order to maximize area?
a. 2 ft by 13 ft
c. 7.5 ft by 7.5 ft
b. 4 ft by 11 ft
d. 10 ft by 5 ft
Copyright © 2009 Pearson Education, Inc. Slide 3 - 33
The Cotes have 30 feet of picket fence with which to enclose a flower garden. What dimensions should the garden have in order to maximize area?
a. 2 ft by 13 ft
c. 7.5 ft by 7.5 ft
b. 4 ft by 11 ft
d. 10 ft by 5 ft
Copyright © 2009 Pearson Education, Inc. Slide 3 - 34
Solve:
a. 3
c. 1
b. 3, 7
d. 7, 3
3 111.
5 3 1x x
Copyright © 2009 Pearson Education, Inc. Slide 3 - 35
Solve:
a. 3
c. 1
b. 3, 7
d. 7, 3
3 111.
5 3 1x x
Copyright © 2009 Pearson Education, Inc. Slide 3 - 36
Solve:
a. 2
c. 14
b. 4
d. 16
2 8 6 10.x
Copyright © 2009 Pearson Education, Inc. Slide 3 - 37
Solve:
a. 2
c. 14
b. 4
d. 16
2 8 6 10.x
Copyright © 2009 Pearson Education, Inc. Slide 3 - 38
Solve:
a. 25
c. 5
b. 5, 69
d.
6 2 2 2.n
1
3
Copyright © 2009 Pearson Education, Inc. Slide 3 - 39
Solve:
a. 25
c. 5
b. 5, 69
d.
6 2 2 2.n
1
3
Copyright © 2009 Pearson Education, Inc. Slide 3 - 40
Solve:
a.
c.
b.
d. 3
3 2 11.x
13
3
13,3
3
3 1,
13 3
Copyright © 2009 Pearson Education, Inc. Slide 3 - 41
Solve:
a.
c.
b.
d. 3
3 2 11.x
13
3
13,3
3
3 1,
13 3
Copyright © 2009 Pearson Education, Inc. Slide 3 - 42
Solve:
a.
c.
b.
d.
8 3 7.m
1 5,
2 4
1
2
1 5,
2 4
5
4
Copyright © 2009 Pearson Education, Inc. Slide 3 - 43
Solve:
a.
c.
b.
d.
8 3 7.m
1 5,
2 4
1
2
1 5,
2 4
5
4
Copyright © 2009 Pearson Education, Inc. Slide 3 - 44
Solve:
a.
c.
b.
d.
6 5.x
, 11 1,
,1 11,
1,11
11, 1
Copyright © 2009 Pearson Education, Inc. Slide 3 - 45
Solve:
a.
c.
b.
d.
6 5.x
, 11 1,
,1 11,
1,11
11, 1
Copyright © 2009 Pearson Education, Inc. Slide 3 - 46
Solve:
a.
c.
b.
d.
4 12.x
, 8 16,
, 16 8,
8,16
8,16
Copyright © 2009 Pearson Education, Inc. Slide 3 - 47
Solve:
a.
c.
b.
d. [8, 16]
4 12.x
, 8 16,
, 16 8,
8,16
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