CHAPTER 5 The Quadratic Formula
The main focus of this chapter is to learn how to use one of the most basic, most
widely used and most important formulas in algebra namely the quadratic formula. We
will develop this formula in section 5.2 and use it to so

CHAPTER 4
Section 4.3
1.
5.
9.
13.
5 = |x - 3|
3.
4 = |x + 2|
= |x - a|
7.
x = 4, x = -2
x = -1, x = -3 11. x = 4, x = 0
x = 5, x = -1 15.
x = + 1, x = -1
17.
(x 4)
f (x) | x 4|
(x 4)
19.
x 1 if x 1 0
f (x) | x 1|
x 1 if x 1 0
if x 4 0
if x 4 0
21.

Chapter 5
Section 5.4
1.
two distinct complex roots
3.
two distinct real (irrational) roots
5.
two distinct complex roots
7.
one rational root
9.
c = 9/4
13.
c 9/4
17.
c > 9/4
11.
15.
19.
c = 9/8
c 9/8
c >9/8

Chapter 5
Section 5.6
1.
Complete the square in ax2 + bx + c:
b
b
b2
x ( )2 )
c
a
2a
4a
=
b 2 b2
a(x
)
c
2a
4a
=
b 2
b2
a| x
| (
c)
2a
4a
=
2
a(x
f(x)
With this last expression for f(x), the y-coordinate of any point on the graph of y = f(x)
depends

Chapter 6
Section 6.2
1.
asymptote at x = -2;
x-intercept = none
horizontal asymptote at y = 0;
3.
vertical asymptote at x = 10;
x-intercept = none
horizontal asymptote at y = 0;
y-intercept = -1/5
5.
vertical asymptote at x = 5;
x-intercept = none
horizo

Chapter 6
Section 6.1
1.
polynomial of degree 1
3.
not a polynomial
5.
not a polynomial
7.
polynomial of degree 3
9.
rational function
11.
not a rational function
13.
domain = all real; f(0) = 5, f(_R(2) = 5
15.
domain = all real; f(0) = -3, f(3) = 18
-1

Section 6.4
1.
3.
5.
The graph looks just like the graph of y =
1
, but their is one exception.
x-6
A close-up at x = -1 reveals that there is a gap at the point (-1, -1/6). This is due to the fact
that the original expression for y has two factors of x +

Section 6.5
1.
Using the font (Geneva) that most of this book is printed in , following letters have a line of symmetry:
Vertical line through the center: A, H, I, M, O, T, U, V, W, X, Y
Horizontal line through the center: C, D, E, H, I, X
Note: Upon clos

CHAPTER 7
Section 7.1
1.
y = (1/3)x
y = 3x
3.
y = 5-x
y = 5x
5.
y = 1.2-x
y = 1.2x
7.
y=
1
( 2 )x
y=
y = 2x+2 y = 2x
9.
y = 5x+2 y = 5x
11.
13.
2x
y = 4-x-1
y = 4x
y = 5x-1
y = 2x - 3

CHAPTER 7
Section 7.2
1.
The first generation of 100 couples produces two children or one couple and so in the second
generation, there are 100 couples. The 200 couples that now inhabit the planet each produce a
couple, and so there are 400 couples on the

Section 5.4 The Theory of Quadratic Equations
(The Discriminant)
Key Words: Discriminant
Goals. In this section we will provide you with further insight into the structure of the quadratic
formula and how the solutions to a quadratic equation are classifi

Section 5.3 An Introduction to Complex Numbers
Goals. Our goal in this section is to give you enough familiarity with complex numbers so that you
can find solutions to any quadratic equations.
The equation x2 + 1 = 0 is easy to solve using the quadratic f

5.5 Quadratics in Disguise
Key Concepts: Skeleton of an equation, Quadratic in another variable
Goals. Our goal in this section is to expose you to equations that do not appear to be quadratic upon
first examination, but are indeed quadratic in that they

Section 5.2 The Quadratic Formula and Its Use
Key Words: rational, irrational
Goals. Now that you have an appreciation for how quadratic equations are solved we will show you
how to condense the work that is needed to obtain solutions by introducing the q

Section 5.6 More Problem-Solving with Quadratic Functions
Goals. Our goal in this section is to provide you with an opportunity to use the tools that are provided
in this chapter. Our first objective is to show you some examples of these tools in action,

Chapter 6 Curve Sketching and Rational Functions
6.1 Polynomials and Rational Functions
Key Words: polynomial, degree, rational, domain, range, implied domain
Key Concepts: domain, range
Goals. Our goal in this section is to introduce the general form of

6.2 Graphing Basic Rational Functions
Key Words: asymptote
Goals. Our goal in this section is to introduce the graphs of some of the most frequently encountered
rational functions. We hope that by the end of this section, you are familiar not only with th

Section 6.3 Transformations of Graphs
Key Words: transformation, translation
Key Concept: knowledge of simple graphs can be be utilized to sketch more complicated graphs.
Goals. Our goal in this section is to reinforce the idea of a family of graphs. We l

6.4 Graphing More Rational Functions
Goals. Our goal in this section is, as in the previous section, to sketch rational functions using an
analysis approach rather than plotting point by point. After the analysis that we suggest, plotting a few
well-chose

Section 6.5 Symmetry
Key Words: Symmetric
Key Concepts: Symmetry with respect to a line or a point
Goals. Symmetry is a geometric notion that is an aid in the description of certain objects such as
graphs. In this section, we will discuss the main types o

6.6 Stretching and Shrinking of Graphs
Goals. Our goal in this section is to show you how graphs can be stretched or shrunk in either the
vertical or horizontal direction. We close with a summary of the transformations that you should know.
Let us now put

Chapter 7 - Exponential and Logarithmic Functions
Section 7.1 The Exponential Functions
Key Words: exponential, base
Goals. Exponential functions have a wide variety of applications ranging from population growth
problems to banking. In this section the s

Solutions to Exercises in Section 3.5
1.
3 seconds. The exact value is less than 3 seconds.
2.
2 5 4.5 seconds
3.
1/8 sec.
4.
30
1.37 sec
4
5.
10 seconds
6.
0.7 seconds (The exact value, neglecting air resistance is slightly less)
7.
80.6 feet per second