Warm-up
5.1 Notes
Modeling Data w/Quadratic Functions
Evaluate each function for x = -3 and x = 3 1) 2)
f ( x) = x 2
f ( x) = 12 x 3
3)
1 f ( x) = x 2 3
Quadratic Functions and Their Graphs
OBJECTIVES: identify quadratic functions and graphs model data wi
Warm-up
5.2 Notes
Find the y-intercept of the graph of each function. 1) y = 3x + 3 2) 4x 3y = 12
Find the vertex of the graph of each function. Properties of Parabolas 3) y = | -2x | 4) y = | 3x +7 |
Graphing Parabolas
Objectives: - graph quadratic funct
Objective
5.5 Notes (continued)
- To solve quadratic equations by graphing.
Quadratic Expressions
Solving by Graphing
Not every quadratic equation can be solved by factoring or taking the square root. You can solve by graphing a quadratic equation and loo
5.6 Notes
Objectives:
to identify and graph complex numbers to add, subtract, and multiply complex numbers.
Complex Numbers KEY TERMS: -imaginary number -complex numbers
Identifying Complex Numbers
In Chapter 1 we classified all types of REAL numbers. (na
Warm Up
1) Write the equation in standard form:
Objectives
To use the Quadratic formula to find the zeros of an equation. To understand the Discriminant of an equation. KEY TERMS The Quadratic Formula The Discriminant
y = 2 x ( x 1) + ( x + 1) 2
2) Eva
STATION 1 Writing a Quadratic Model Standard Form *When you are given three points and told to write a quadratic model, youll have to use standard form unless you know that one of them is the vertex. Standard Form y = ax 2 + bx + c Directions: Use the thr
Lesson: Square Roots and Radicals Name_ Objectives: -review properties of square roots -simplify radical expressions Radical Symbol: 16 means the positive square root of 16. 16 means the negative square root of 16. Properties: Multiplication Property of S
Obejctives Section 6.2
Zeros of polynomial functions Find the zeros (and their multiplicity) of a polynomial function Understand the relationship between zeros, roots, solutions, x-intercepts and factors of a polynomial
What is the difference between a po
Objectives
Section 6.3 part 1
Polynomial long division
Divide polynomials Use polynomial division to determine if a linear expression is a factor of a given polynomial. Key Terms Divisor Dividend Quotient Remainder
Review
Remember long division?
Divide x
Hw #12 p311 17-31odd, 35 p 318 (1-4)
Free Throws! I have an idea
During 2nd semester, we will do a total of 30 free throws (maybe more) It will be worth 20 points in the test/quiz column Ill keep a running tally of what you have in an inactive assignment.
Objectives
Factor the sum and difference of cubes (and use this factoring to solve polynomial functions) polynomial Factor polynomials that are quadratic in form Solve Polynomial equations using a graphing calculator graphing
Section 6.4
Solving polynomia
Objectives
Understand the implications of the fundamental theorem of algebra Find ALL the roots to a given polynomial equation
Section 6.6
THE FUNDAMENTAL THEOREM OF ALGEBRA
Carl Friedrich Gauss
In 1799 Gauss proved that if you solve any polynomial equati
OUTLINE
Homework (and homework questions) Homework Ask any review questions you want Ask Review long division, solve by factoring and graphing calculators and BREAK 6.5 Notes (not on quiz) 6.5 Homework time / study time Homework
Homework:
Quiz Friday! Abo
Algebra II Ch 6 Test Study Guide Answers are on my door AND online starting Friday
Name: _ Per: _
Classify the polynomial by degree and by number of terms. 1) y = x 5 x + 2 1) _ Write the polynomial function in factored form. 2) f ( x) = 125 x 3 + 64 2) _
Objectives
Section 6.8
Expanding Binomials & Pascals Triangle
Use Pascals Triangle to expand a binomial
Recall
( x 3) 2 IS NOT x2 9
Lets look for a pattern
(a + b) 2 = (a + b)(a + b) = a 2 + 2ab + b 2 (a + b) 3 = ( a + b)(a + b)(a + b) =
( x 3) 3 IS NOT
Warm up
Section 6.1
Multiply
x(3 x 2 + 5)( x - 1)
( x - 2) 3
Polynomial Functions
Objectives
Classify polynomials by degree and by number of terms Write polynomials in standard form and factored form
Definition of a Polynomial Function
P ( x) = an x n + a
Obejctives Section 6.2
Zeros of polynomial functions Polynomial Division Find the zeros (and their multiplicity) of a polynomial function Understand the relationship between zeros, roots, solutions, x-intercepts and factors of a polynomial
What is the dif
Objectives
Divide polynomials Use polynomial division to determine if a linear expression is a factor of a given polynomial. Key Terms Divisor Dividend Quotient Remainder
Review
Remember long division?
5 1684
5 40
We use division to find factors of real n
Carl Friedrich Gauss
In 1799 Gauss proved that if you solve any polynomial equation, your roots are included in the complex numbers. This seems obvious, but the idea was so iimportant that we so mportant call it THE FUNDAMENTAL THEOREM OF ALGEBRA. THEOREM
Algebra II Ch 6 Test Study Guide Answers are on my door AND online starting Friday
Name: _ Per: _
Classify the polynomial by degree and by number of terms. 1) y = x 5 x + 2 1) _ Write the polynomial function in factored form. 2) f ( x) = 125 x 3 + 64 2) _
Algebra II Ch 6 Test Study Guide Answers are on my door AND online starting Friday
Name: _ Per: _
Classify the polynomial by degree and by number of terms. 1) y = x 5 x + 2 1) _ Write the polynomial function in factored form. 2) f ( x) = 125 x 3 + 64 2) _
Objectives
Section 6.5
Rational Root Theorem!
Use the rational, irrational, and imaginary root theorems to locate all the roots of a all the given polynomial equation given
Rational Root Theorem
This only works if we have integer coefficients. coefficient
Algebra II 6.1 6.4 Quiz Show all work to receive Credit Form A
Name: _ Per: _
Write each polynomial in standard form. Then classify it by degree and by number of terms. 1) x( x 1) 3 2) (7 x 2) ( x 2 + 8 x 1)
Standard Form: Classify:
Standard Form: Classif
1.6 Notes: Probability Warm-up Write each number as a percent.
1)
3 8
2) 0.0043
3) 1
5 6
Objective: - to find experimental probabilities - to find theoretical probabilities Experimental Probability The experimental probability of event = P(event) = number
Algebra II guided notes 7.1
Name: _
DIRECTIONS: Read pages 363-365 in your book and fill in this handout. When you are done, try the sample problems on the back. This will count as a class-work assignment. I. Roots and Radical Express Since 5 2 = 25 , 5 i
Algebra II Chapter 1 test checklist 1) Be able to expressions involving absolute value a. - 4 + (-11) - 4 + (-11)
Name: _ b. - 20 - 22 5
2) Be able to simplify and combine like terms 1 a. - ( x - 2) - ( x - 9) 3
b. 3 x - y - 6 x + 2 y
3) Be able to evalua
7.3 Binomial Radical Expressions
Warm Up
8 + 6 2 3 28 = ?
3
23 8 4 23 = ?
Objective
To Add & Subtract Radical Expressions To Multiply & Divide Binomial Radical Expressions
Adding Radical Expressions
Its the same rules used for integers!
8 3 x + 5 3 x
Si
Section 2-1 Relations and functions Warm up Evaluate each expression for x = 2, 1, and 0. 1)
- ( x - 2)
2)
2x2 + 1
Objectives: - Graph relations - Identify Domain and Range - Identify Functions Relation
Example Suppose you use a motion detector to track