10.1 Adding and Subtrac2ng
Polynomials
Mrs. Suchodolski
Algebra 1
Vocabulary
1. A polynomial is an expression which is the
sum of terms of the form axk where k is a
nonnega2ve integer.
2. A polynomial is wriDe
15.2 One-
Way Analysis of Variance
(ANOVA)
Mrs. Suchodolski
AP StaBsBcs
The Goal
To compare several means.
Examples: Highway gas mileage for 1998
model vehicles (midsize, pickup, SUV)
Stemplots for Vehicle
2
10.5 Factoring x + bx + c
Mrs. Suchodolski
Algebra
Vocabulary
To factor a quadra@c expression means to
write it as the product of two linear
expressions.
You know from the FOIL method that
(x + p
10.4 Solving Polynomial
Equa5ons in Factored Form
Mrs. Suchodolski
Algebra
Vocabulary
Factored form: A polynomial is in factored
form if it is wriGen as the product of two or
more linear factors.
Standard form
Mrs. Suchodolski
The discriminant is the expression inside the
radical in the quadratic formula.
2
b 4ac
The discriminant can be used to find the
number of solutions of the quadratic
equation.
Consider the quadratic equation:
2
2
ax + bx + c = 0
1. If
Mrs. Suchodolski
2x2 + 10 = 28
- 10 -10
2x2 = 18
x2 = 9
x = + 3 These are the solutions/roots of the equation.
We did not need the quadratic formula to
solve this quadratic equation because it was
in the form
ax2 + c = #
where b = 0.
It
is a formula used
9.4 Solving Quadra2c
Equa2ons by Graphing
Algebra
Ms. Malloy
Solving Quadra2c Equa2ons Using
Graphs
The solu2on of a quadra2c equa2on in one
variable x can be solved or checked graphically
with the following step
9.3 Graphing
Quadratic Functions
Mrs. Suchodolski
Quadratic Function Properties
A quadra2c func2on is a func2on that can
be wri9en in the standard form
y = ax2 + bx + c where a
Mrs. Suchodolski
What is it?
A quantity is decreasing exponentially if it
decreases by the same percent in each unit
of time.
The Model
y = C(1 r)t
C = the initial amount
t = the time period
r = th
8.5 Exponential Growth
Functions
Mrs. Suchodolski
What is exponential growth?
A quantity is growing exponentially if
it increases by the same percent in
each unit of time.
The Model
y = C(1 + r)t
C = the initial amount
t = the time period (how much time h
Mrs. Suchodolski
Numbers such as 1,000,000, 153,000 and
0.00009 are written in standard form.
Another way to write a number is to use
scientic notation.
n
c x 10
where 1 c < 10 and n is an integer
St
8.4
Logarithmic Functions
Mrs. Suchodolski
Think about 2x = 6.
We cant calculate the exact value in our
heads, but we could give an interval for x.
l To find the exact value of x, we will use
logarithms.
l
Definition of a logarithm with
base b.
Let b and
Mrs. Suchodolski
Much of the history of mathematics is marked
by the discovery of special types of numbers
like counting numbers, zero, negative
numbers, pi, and imaginary numbers.
Like
pi and i, e denotes a number.
Called The Euler Number after
Leonha
P. 474
Has
the same form as
growth functions f(x) =
abx where a > 0 BUT:
0 < b < 1 (a fraction
between 0 and 1)
State whether f(x) is an exponential
growth or decay function
1. f(x) = 5(2/3)x
b=2/3, 0<b<1 it is a decay function.
2. f(x) = 8(3/2)x
b= 3/
8.1 - Exponential Growth
Mrs. Suchodolski
Exponential Function
y = ab
x
b > 1
The graph passes through the point (0, a).
So, the y-intercept is a.
The x-axis is an asymptote of the graph
(y = 0 is an asymptote).
The domain is all real numbers.
The rang
7.4 Inverse Functions
Mrs. Suchodolski
Review from chapter 2
Relation a mapping of input values (x-values)
onto output values (y-values).
Here are 3 ways to show the same relation.
y = x2
Equation
Table of
values
Graph
x
y
-2
4
-1
1
0
0
1
1
Inverse rel
Solving Systems of Linear Equations
Solve by graphing
Write equations in slope intercept form: y = mx + b
Begin with b graph the y-intercept (0, b)
Move m the slope rise/run
o If positive move the rise units up and run units to the right
o If negative
Algebra 1: Properties of Exponents
Definitions:
An expression like 46 is called a power.
The exponent 6 represents the number of times the base 4 is used as a factor.
Properties:
Product of Powers: am an = am+n
example: 35 36 = 35+6 = 311
Power of a Pow
Planning a Sundae Party (40 people)
Item
Number of each
Ice Cream and Serving Items
Icecream gallon top
brand
Icecream gallon
store brand
Icecream 1 gallon top
brand
Icecream 1 gallon
store brand
50 plastic bowls
24 plastic spoons
100 Napkins
Serving spoo
Name: _
Period: _
Pi Day Project (60 Points)
3.141592654
Due Pi Day (Thursday March 14, 2013)
Pi day is Thursday, 3/14! In honor of this special day, we will be creating projects. You have a
choice of projects. Projects must be neat, well organized, color
Name: _
Period 11: Algebra 1
Due: February 28, 2013
Modeling Real-Life Problems as Linear Equations
This project is to create a business and model it with a linear function. (50 points)
A. You are to come up with a business that you can start. Your projec
Intermediate Algebra 1
MP 4 Project
Due on Tuesday, 5/14
Name _
STAINED GLASS PARABOLAS
1. Make up 4 quadratic equations, labeling them 1, 2, 3 & 4.
2. Two of the graphs must open up and two must open down.
3. For each equation, find the vertex, the axis
GAME PROJECT
Name:
Due Date: Friday, June 14th, 2013
(10 points off for entire group for each day late)
Create a game using at least 4 sections from our textbook (chapters 8 - 12)
only.
Your project MUST include:
1. A new and different name for your game.
Solving linear equations with variables on both sides
1. Write the original equation
ax +b = cx + d
3x + 5 = -2x + 15
2. Simplify the expression on the left side of the equal sign
a) Use order of operations (PEMDAS)
b) Distribute to remove parenthesis
c)
Name _
Study Guide 2.2 to 2.7, Properties of Real Numbers
Date _
1. Addition, SAME sign: add the numbers keep the sign
8 + 6 = 14
-8 + (-6) = -14
2. Addition, DIFFERENT sign: take difference of the two numbers, keep sign of larger
number
-8 + 6 = -(8 6) =
Name _
Study Guide 1.1 to 1.3 (Order of Operations)
Date _
Period 11: Int. Algebra 1
1. Redo problems from the homework and the review sheet.
2. Expressions may not contain the equal sign (=) or any type of inequality.
3. An equation is a mathematical sen
Probability
Day 2 - Factorial
Order matters: ex: finishing a race
Counting Principle:
Order does not matters:
Example packing a suitcase, toppings
on a pizza
2 colors: black (26) red (26)
4 suits: clubs (black, 13) spades (black, 13)
hearts (red, 13) dia