Algebra II 100
10-5 Algebra Theorems
Name: _
Fundamental Theorem of Algebra
Every polynomial equation of degree 1 or more has at least one solution in the set of
complex numbers.
Corollary
If P(x) is an nth degree polynomial, then P(x) has exactly n linea
Advanced Linear Inequalities
Introduction: In Unit 1, you learned both simple and compound inequalities.
Hopefully, you noticed that a compound inequality is comprised of two parts. In this
lesson, we will be looking
9.3 Graphing General Rational Functions
Let p(x) and q(x) be polynomials with no common factors other than 1.
p( x ) am x m + am 1 x m 1 + . + a1 x + a0
=
The graph of the rational function f ( x ) =
q( x )
bn x n + bn 1 x n 1 + . + b1 x + b0
has the foll
9.2 Graphing Simple Functions
y=
y=
y=
a
x
Hyperbola shape
X-axis is a horizontal asymptote
Y-axis is a vertical asymptote
Domain and range are all nonzero real numbers
a
+k
xh
Vertical asymptote at x=h
Horizontal asymptote at y=k
ax + b
cx + d
Vertical a
Alg II
Date: _
Lesson 9.1 Inverse and Joint Variation
VOCABULARY:
Inverse variation: is the relationship of two variables x and y if there is a
k
nonzero number k such that xy = k, or y =
x
Constant of Variation: The nonzero constant k.
Joint Variation: o
Alg II
Date: _
Lesson 8.1 Exponential Growth
VOCABULARY:
Exponential Function : involves the expression bx where the base is b is a
positive number other than 1. If a > 0 and b > 1, the function y = abx is an
exponential growth function.
Asymptote: is a l
CP Algebra II
Date: _
Lesson 7.1 Notes nth Roots and Rational Exponents
For an integer n greater than 1, bn = a, then b is an nth root of a. An nth root of
a is written as
n
a , where n is the root index of the radical.
Real nth Roots
Let n be an integer
CP Algebra II
Date: _
Lesson 6.1 Notes Using Properties of Exponents
VOCABULARY:
Scientific Notation: A number is expressed in Scientific notation if it is in the
form c x 10n where 1 c < 10 and n is an integer.
Properties of Exponents
Example 1: Evaluati
CP Algebra II
Date: _
Lesson 5.1 Notes Graphing Quadratic Functions
VOCABULARY:
Quadratic function has the form ax2 + bx + c where a 0.
Parabola The U-shaped graph of a quadratic function.
Vertex The lowest or highest point on the graph of a quadratic fun
CP Algebra II
Date: _
Lesson 4.1 Notes Matrix Operations
VOCABULARY:
Matrix: A rectangular arrangement of numbers in rows and columns
Dimensions of a matrix: The number of rows m of a matrix by the number of columns n
of the matrix, written m x n.
Entries
The Devil and Tom Walker by Washington Irving
Please answer the questions assigned to your group with detailed evidence. We will present these to the
class for discussion.
1. What is the setting of Irvings story? Remember to include time and place(s).
2.
NAME:
DATE:
PAGE #
HONORS English 11
Questions The Devil and Tom Walker
Answer each of the following questions in complete sentences.
1.
Why does Tom Walker refuse the devils first offer?
2.
Identify three of the stories explaining the disappearance of
To
Reading Comprehension Questions:
The Devil and Tom Walker (177)
1. What is the setting for this story? What is supposed to be hidden under one of the
big trees beside the inlet? What happened to the person who hid it there? Who
supposedly presided
Few mil
Study Questions: The Devil and Tom Walker
1. What is the setting (place, year and description of forest)
2. Specifically describe the stranger (devil) (p. 231)
3. What does the comment about earthquakes imply about their cause? (p. 229)
4. What word descr
CP Algebra II
Date: _
Lesson 1.1 Notes Real Numbers and Number Operations
Subsets of the Real Numbers
WHOLE NUMBERS 0, 1, 2, 3, . . .
INTEGERS . . . , -3, -2, -1, 0, 1, 2, 3, . . .
1 1 4
RATIONAL NUMBERS Numbers such as , ,
(or 4) that can be
231
written
CP Algebra II
Date: _
Lesson 2.1 Notes Functions and Their Graphs
VOCABULARY:
Relation: A pairing of input values with output values.
Domain of a relation: The set of input values for a relation.
Range of a relation: The set of output values for a relatio
Algebra II Honors
10-4 C Worksheet Answers
1. d
2. c
3. b
7. y = ( x + 1)3 ( x 3)2
8. y = ( x + 1)3
9. y = ( x + 5) 2 ( x + 3) 2
10. y =
1
x ( x 3) ( x 5) ( x 1)
12
11. y = ( x 1) ( x + 2)
12. y = ( x + 2)2 ( x 2)
13. y = x 2 ( x 5)2
14. y = ( x + 2) ( x
Algebra II Honors
10-4 B answers day 2
Name: _
y
y
5)
y
6)
9)
x
x
x
y
y
10)
y
11)
12)
x
x
x
y
y
15)
16)
x
20) y = x( x + 2) 2
23)
3
y = ( x + 4)( x 2)
8
x
21) y = ( x + 3) 2 ( x + 1)( x 1)
24)
y = x( x 1)( x 2)
22) y = x 2 ( x 3)2
Algebra II Honors
10-4B Worksheet Answers
Name: _
y
y
y
1)
2)
3)
x
x
x
y
y
4)
y
7)
8)
x
x
x
y
y
5
13)
14)
-2
2
4
6
x
-5
x
-10
-15
-20
-25
19)
23)
24)
y = -(x + 3)(x + 1)(x 1)
3
y = ( x + 4)( x 2)
8
y = x( x 1)( x 2)
y
5
25) (-1, 3), (0, 0) & (1, -3)
-3
-2
Algebra II Honors
10-3 Sum & Product of Roots notes
Name: _
For each of the following, solve by factoring.
1) x 2 8 x + 15 = 0
2) x 2 + 2 x 3 = 0
3) 2 x 2 3 x 2 = 0
4) 6 x 2 + 7 x 3 = 0
For each of the following, solve by completing the square or quadrati
Algebra II Honors
9-8 Systems of Conics notes
Solve the systems of equations or inequalities.
1)
Name: _
y
x 2 y 2 = 16
x y = 2
x
y
2)
x 2 + y 2 25
2
y > x
x
y
3)
2 x 2 + 3 y 2 = 22
2
2
x + y = 9
x
4)
x2 y2 = 1
2
y = 1 x
y
x
y
5)
x2 + y 2 = 9
2
2
x
Algebra II Honors
9-5 Parabola
Name: _
Definition of Parabola
A parabola is the set of all points in a plane that are the same distance
from a given point called the focus and a given line called the directrix.
Information about Parabolas
y = a ( x h) 2 +
Algebra II Honors
9-4 Writing Equations of Hyperbolas
Name: _
Class Notes
Write an equation of the hyperbola with the given properties.
1)
center = (3, -2)
focus = (3, 1)
hyperbola is tangent to x-axis
2)
vertices = (-2, 0) & (-2, -6)
slope of asymptotes
Algebra II Honors
9-4 Hyperbolas ws #2 answers
1)
a)
b)
c)
d)
C = (0, 0)
V = (0, 4)
F = (0, 2 5)
y = 2 x
Name: _
2)
y
a) C = (1, 2)
b) V = (7, 2) (-5, 2)
c) F = (11, 2) (-9, 2)
d)
4
2
y= x+
3
3
4
10
y=
x+
3
3
y
3)
5
a) C = (0, -5)
b) V = (0, -1) (0, -9)
c
Algebra II Honors
1)
9-4 Hyperbolas Answer Key
a) C = (0, 0)
b) V = (8, 0)
c) F = ( 89, 0)
5
d) y = x
8
y
2) a) C = (6, -2)
b) V = (6, 2) (6, -6)
c) F = (6, -2 41 )
d)
4
34
y= x ;
5
5
4
14
y = yx +
5
5
y
10
5
5
5
-5
- 10
-5
5
10
5
10
15
x
-10
x
-5
5
-5
10