3.3 Zeros of Polynomial Functions
Consider the polynomial function = % + 2,
written in its factored form = ( 1)( + 2).
If we solve the individual factors you have x = 1 and x = 2.
These values make the function equal to zero, so they are
3.4 Polynomial Functions: Graphs, Applications, and Models
Graphs of f ( x ) = ax n
Each figure above has an odd degree and is an odd function
(highest power is odd) exhibiting symmetry about the
origin. Each has domain of all rea
Section 3.5
A rational function is a function where both the numerator
and the denominator are polynomials.
Asymptotes
An asymptote is a line that a curve approaches as it heads
towards infinity.
1
1.6 Other Types of Equations
A rational equation is an equation that has a rational
expression (fraction) for one or more terms.
To solve a rational equation, multiply each side by the
least common denominator (LCD) of the terms of the
e
2.6 Graphs of Basic Functions
Continuity
Continuity (Informal Definition)
A function is continuous over an interval of its domain if its
handdrawn graph over that interval can be sketched
without lifting the pencil from the paper.
If a functi
Section 3.1
Polynomial functions are used to model many practical
applications.
In this section we will be concentrating on quadratic
functions (degree 2).
1
The graph of a quadratic function is a para
Section 2.3: Functions
We often describe one quantity in terms of another such
as
The letter grade you receive in a mathematics class
depends on your numerical scores.
ones educational level is linked to their income
A relation is a corr
Polynomials
Monomials single term such as 2x
Binomials two terms such as 2x + 3
Trinomials three terms such as 2x2 + 3x + 4
Before we talk about factoring polynomials, we need to review
some about multiplying polynomials.
To multiply polynomials
Section 2.4
Linear functions
Before we begin our discussion about linear functions, we
will review how to draw the graphs of lines.
Graph f(x) = 2x + 6. Give the domain and range.
1
3
Graph f(x) = x + 6. G
1.4 Quadratic Equations
Quadratic Equation in One Variable
An equation that can be written in the form
ax2 + bx + c = 0, where a, b, and c are real numbers with
a 0, is a quadratic equation. The given form is called
standard form.
A quadratic
Section 2.5 Equations of Lines and Linear Models
Vertical and Horizontal Lines
Equations of Vertical and Horizontal Lines
The equation of a vertical line through the point (a, b) is
x = a.
The equation of a horizontal line through the point (
MATH 1314
REVIEW TEST 1
Solve by factoring and the zerofactor product.
1.
2x2 = 18x 36
Solve using the square root property.
3.
x2 = 16
Solve using the quadratic formula.
5.
x2 14x + 74 = 0
Solve the fol
Section 3.2
A division problem can be written using multiplication,
even when the division involves polynomials.
Divide 356 by 24
1
Divide 3x3  2x2 150 by x 4
2
Remo
Test #3 Review Math 1414
I?1
Name Be;
In order to receive full credit you need to show all work.
Solve the equation by expressing each side as a power of
the same base and then equating exponents.
1)4(1+2><)ns4
mm 3
4+
13:
4.)c,>;:127><1
1.
2 a
(a) =
Test #2 Review Math 1414 171
Name 1; g!
a
In order to receive full credit you need to show all work. 3) f(x) _ x4 _ 4x3 + 4x2 =' KWX " lYail'q')
l
y 7" X cfw_1'40
Complete the following:
(3) Leading Coefficient, Degree, 8: the end behavior.
(b) Find the
Test #1 Review Math 1414
171
Name Kg T/ _ _
In order to receive full credit you need to show all work.
Simplify.
1) 22  32+3(42 12)2+2
: 2a3+3(bra)1.;.g
= 22 5+5(4)3;z
=32q+3UM2
=32 CI~t48:9.
:22 0: +2Lt
= 15 Ht
Eil
Solve the equation. LCD: l3
2) 7
Fraction to Decimal Conversion Table
fraction  decimal I
in
 E
 a:
Oilh
= 0.8
bu'hu
MIA gala U'IIl NA w_\ Mg AH
II
p o o p c o 
N
01
tD~l DIN 0qu NIUI NIN GIUI UIIN hlw WIN
II
o o p o p o o o o
N
00 
01
\l
A
h
= 428
EVEN FUNCTIONS:

Exponents are even
End behavior is the same for the
left and the right
Negative leading coefficient will
switch the end behavior
a>0
a<0
EVEN ROOTS:

Multiplicity is even
Graph will bounce at zero
ODD FUNCTIONS:

Exponents are odd
End
Graph of Polynomial Function:
Function:
2) Find xintercepts:
1) Degree:
3) Find yintercepts:
5) Determine the number of turning points:
4) Determine multiplicity/behavior of xintercepts:
6) Determine end behavior:
7) Create table of points:
8) Graph fun
Fractions
A fraction is a part of a whole
Slice a pizza, and you will have fractions:
1
1
/2
(OneHalf)
3
/4
(OneQuarter)
/8
(ThreeEighths)
The top number tells how many slices you have
The bottom number tells how many slices the pizza
wascut into.
Equi
Translating Word Problems
Word List:
Addition
Add
Sum
*More than
Total
Increased by
Subtraction
Subtract
Difference
Less
*Less than
Decreased by
Minus
*Subtracted from
Exponent(Power)
Squared (2nd power)
Cubed (3rd power)
Fourth power (4th power)
Multipli
Greatest Common Factor
The highest number that divides exactly into two or more numbers.
It is the "greatest" thing for simplifying fractions!
Let's start with an Example .
Greatest Common Factor of 12
and 16
Find all the Factors of each
number,
Circle th
Adding Fractions with Different Denominators
But what if the denominators (the bottom numbers) are not the same? As in
this example:
3
/8
+
1
/4
+
=
?
=
You must somehow make the denominators the same.
In this case it is easy, because we know that 1/4 is
538 I Chapter 6 Systems of Equations
El
" PR DJ E 0 T5
1. FINDING ZEROS OF A POLYNOMIAL One zero of c. What is the slope of the line betweenO and P?
P(x) = x3 + 2x2 + Cx 6 is the sum of the other two . , . _ .
zeros of Pa). Find C and the three zeros of
Conic Sections
Standard Forms of the Equation of a Parabola
Equation
Vertex
Focus
Directrix
Axis of Symmetry
Opens
x 2 = 4 py y 2 = 4 px ( x  h) 2 = 4 p ( y  k ) ( y  k ) 2 = 4 p ( x  h)
(0, 0) (0, 0) (h, k )
(0, p) ( p, 0) (h, k + p )
Name_
6.1: Conic Sections
PARABOLA
A parabola is the set of points in the plane that are equidistant from a fixed line (the directrix) and a fixed point (the focus) not on the directrix.
The midpoint of the line segment between the focus and the d