Test Wednesday Review Answers.

Slides:

Advertisements

Similar presentations

Section 1.4 Complex Numbers

Advertisements

Remainder/ Factor Theorem End Behavior Zeros PolynomialsGrab.

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

4.3 – Location Zeros of Polynomials. At times, finding zeros for certain polynomials may be difficult There are a few rules/properties we can use to help.

Power Functions and Models; Polynomial Functions and Models February 8, 2007.

7. Roots and Radical Expressions

Lesson 1-5 The Complex Numbers. Objective: Objective: To add, subtract, multiply, and divide complex numbers.

6.2 Graphs of Polynomials. The Degree of Polynomials The degree of a polynomial is the value of the largest exponent. y = 5x 4 + 3x 2 – 7 Degree = 4 y.

5.6 Complex Numbers. Solve the following quadratic: x = 0 Is this quadratic factorable? What does its graph look like? But I thought that you could.

1.4 – Complex Numbers. Real numbers have a small issue; no symmetry of their roots – To remedy this, we introduce an “imaginary” unit, so it does work.

Lesson 4-1 Polynomial Functions.

Complex Zeros; Fundamental Theorem of Algebra

9.9 The Fundamental Theorem of Algebra

Polynomial Functions Zeros and Graphing Section 2-2.

Real Zeros of a Polynomial Function Objectives: Solve Polynomial Equations. Apply Descartes Rule Find a polynomial Equation given the zeros.

Copyright © 2014, 2010, 2006 Pearson Education, Inc. 1 Chapter 3 Quadratic Functions and Equations.

Ch 2.5: The Fundamental Theorem of Algebra

Graphing Polynomials. Step One: Determine End Behavior Using Lead Coefficient Test.

Notes Over 2.8 Rules for Dividing Negative Numbers. ( Same as Multiplying ) If there is an even number of negative numbers, then the answer is Positive.

Complex Numbers, Division of Polynomials & Roots.

Graphing Polynomials. Total number of roots = __________________________________. Maximum number of real roots = ________________________________. Maximum.

WARM-UP: 10/30/13 Find the standard form of the quadratic function. Identify the vertex and graph.

EXAMPLE 5 Use the result to write f (x) as a product of two factors. Then factor completely. f (x) = x 3 – 2x 2 – 23x + 60 The zeros are 3, – 5, and 4.

REVIEW OF UNIT 4.

THE FUNDAMENTAL THEOREM OF ALGEBRA. Descartes’ Rule of Signs If f(x) is a polynomial function with real coefficients, then *The number of positive real.

The Original f(x)=x 3 -9x 2 +6x+16 State the leading coefficient and the last coefficient Record all factors of both coefficients According to the Fundamental.

UNIT 2, LESSON 1 POLYNOMIAL FUNCTIONS. WHAT IS A POLYNOMIAL FUNCTION? Coefficients must be real numbers. Exponents must be whole numbers.

5-2 Polynomials, Linear Factors, & Zeros

5.2 Polynomials, Linear Factors, and Zeros P

Chapter 5.9 Complex Numbers. Objectives To simplify square roots containing negative radicands. To solve quadratic equations that have pure imaginary.

Chapter 4: Polynomial and Rational Functions. 4-2 Quadratic Equations For a quadratic equation in the form ax 2 + bx + c = 0 The quadratic Formula is.

Term 2 Week 7 Warm Ups. Warm Up 12/1/14 1.Identify all the real roots of the equation: 3x x 2 – 9x Identify whether the degree is odd or.

Graphing polynomials To graph a polynomial we need to know three things 1) Type of polynomial 2) Roots 3) y-intercept.

7.5 Roots and Zeros Objectives:

Today in Pre-Calculus Notes: –Fundamental Theorem of Algebra –Complex Zeros Homework Go over quiz.

Functions. Objectives: Find x and y intercepts Identify increasing, decreasing, constant intervals Determine end behaviors.

Chapter 8 Irrational Roots Clark/Anfinson. CHAPTER 8 – SECTION 1 Root functions.

WARM UP- FOR THE POLYNOMIAL LISTED BELOW:. FUNDAMENTAL THEOREM OF ALGEBRA.

Do Now: Solve x2 – 20x + 51 = 0 3x2 – 5x – 2 = 0 Today’s Agenda

Polynomials Graphing and Solving. Standards MM3A1. Students will analyze graphs of polynomial functions of higher degree. a. Graph simple polynomial functions.

PreCalculus 4-R Unit 4 Polynomial and Rational Functions Review Problems.

Grudgeball! Unit 4 (Part 2) Test Review. Factor completely:

SOLVE QUADRATIC EQUATIONS BY USING THE QUADRATIC FORMULA. USE THE DISCRIMINANT TO DETERMINE THE NUMBER AND TYPE OF ROOTS OF A QUADRATIC EQUATION. 5.6 The.

Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.

HOMEWORK CHECK.

Warm Up Evaluate. 1. –24 2. (–24) Simplify each expression.

When solving #30 and #34 on page 156, you must “complete the square.”

7.1 nth roots and rational Exponents

Algebra 2/Trigonometry Name __________________________

Review & 6.6 The Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra

Lesson 2.5 The Fundamental Theorem of Algebra

Polynomial Trashketball

6-8 Roots and Zeros – Day 1 SWBAT

1. Use the quadratic formula to find all real zeros of the second-degree polynomial

Algebra 2/Trigonometry Name __________________________

Polynomial Multiplicity

Warm Up – Look over your notes/examples from last week Any questions??

Analyze Graphs of Polynomial Functions

Graphing Polynomials Unit 1D Day 19.

Graph Polynomials Effect of Multiplicity on a graph

Warm Up Simplify the fraction: a)

5-Minute Check Lesson 4-1.

4.3: Polynomial Functions

Graph Polynomials Effect of Multiplicity on a graph

1) Find f(g(x)) and g(f(x) to show that f(x) and g(x) are inverses

Preview to 6.7: Graphs of Polynomial

Pre-AP Pre-Calculus Chapter 2, Section 5

Presentation transcript:

Test Wednesday Review Answers

Multiplicity Behavior Rules

Factoring Polynomials ed-algebra/graphing-polynomials/

Test Today Pencil Calculator Notecard Everything else off desk

Test Given graph: is it positive, negative, odd, even. What is the degree? Write a possible equation. Given a function (factored): is it positive, negative, odd, even. What is the degree? Sketch a possible graph. Given a function and a root, find the remaining roots. Given a function, find the roots by factoring. Simplify expressions containing imaginary numbers. Find real and complex roots of a given function.