Math Lesson 2-2 Properties of Exponents
|
|
- Eric Greene
- 5 years ago
- Views:
Transcription
1 Math-00 Lesson - Properties of Eponents
2 Properties of Eponents What is a power? Power: An epression formed b repeated multiplication of the base. Coefficient Base Eponent The eponent applies to the number or variable immediatel to its left, not to the coefficient!!!
3 No Eponent? Usuall, we don t write the eponent (saves ink. No Coefficient? * * Usuall, we don t write the coefficient (saves ink. Negative? ( * ( * Usuall, we don t write the coefficient -, we just put the negative smbol (saves ink.
4 Factor: a number that is being multiplied. means base used as a factor times Base Eponent * * * Product: the result ( answer when multipling.
5 Power: is repeated multiplication * * * multiplication: is repeated addition
6 How can ou tell which definition to use? Use the contet of the problem (adding two terms ( ( 7
7 How can ou tell which definition to use? Use the contet of the problem (adding two terms ( ( 5
8 How can ou tell which definition to use? Use the contet of the problem * (multipling two terms ( * ( * * * 5
9 Simplif ( 6 6 (5 50 8
10 Product of Powers Propert ( ( ( * ( * * This is used as a factor how man times? ( ( used as a factor five times 5 When ou multipl powers having the same base, ou add the eponents.
11 Power of a Power Propert ( ( ( * ( * ( * This is used as a factor how man times? ( used as a factor si times * ( 6 6 When ou raise a power to another power ( power of a power ou multipl the eponents.
12 Power of a Product Propert ( ( ( * * * m ( * * * This makes it seem like ou can distribute in the eponent. This onl works with the power of a product! ( You must FOIL the power of a suml!! ( ( m m (
13 ( ( Constants (integer, etc. usuall have an eponent of. 6 8 is a number, we just don t know what it is. You treat all numbers the same (whether the are variables or constants. a b c m ( am bm cm
14 (? **( ( You can re-arrange the order of multiplication. 5 Coefficients of the powers are handled separatel from the base and the eponent.
15 (5 ( 5 0 Simplif: ( 5( * 7 0 ( 5 0 ( 5 5 8
16 What is the difference between? ( and ( and ( and ( and ( (
17 Watch the negatives! (( 6 8 ( ( 6 ( ( Turn negative signs into multiplication b -. This wa ou will be able to tell if the simplified version is positive or negative. Negative coefficients have an eponent of. A negative number raised to an odd eponent remains negative.
18 Your Turn: simplif 6 ( z 8 z ( m 5 0 w 5 ( z 8
19 Negative Eponent Propert Grab and drag * When ou Grab and drag the base and its eponent across the boundar line between numerator and denominator, ou just change the sign of the eponent. Wh do we call this the negative eponent propert?
20 Eamples: 6 6 6
21 Negative Eponent Propert Possible errors * When ou Grab and drag the base and its eponent across the boundar line between numerator and denominator, ou just change the sign of the eponent. DO NOT GRAB the coefficient! *
22 Zero Eponent Propert An base raised to the zero power simplifies to one ( *
23 Combination: ( Negative Eponent, ( Product of Powers, ( Power of a Power, ( Power of a Quotient 6 6 * * 6* * 9
24 Your Turn: 5 ( w z 5 0 w z 5
25 Eamples: Grab and drag Product of powers: add the eponents of same based powers 7 8
26 Your Turn: 5 9( ( (
27 Do ou grab and drag (up or down?? Product of powers propert: add the eponents of like-based powers 6 Product of powers propert: add the eponents of like-based powers 6 Make sure when ou re all done, there are NO NEGATIVE EXPONENTS remaining. 6 It doesn t matter!!!!
Math-2. Lesson:1-2 Properties of Exponents
Math- Lesson:- Properties of Eponents Properties of Eponents What is a power? Power: An epression formed b repeated multiplication of the same factor. Coefficient Base Eponent The eponent applies to the
More informationMath 154 :: Elementary Algebra
Math :: Elementar Algebra Section. Section. Section. Section. Section. Section. Math :: Elementar Algebra Section. Eponents. When multipling like-bases, ou can add the eponents to simplif the epression..
More informationHigher. Integration 1
Higher Mathematics Contents Indefinite Integrals RC Preparing to Integrate RC Differential Equations A Definite Integrals RC 7 Geometric Interpretation of A 8 Areas between Curves A 7 Integrating along
More informationComplex fraction: - a fraction which has rational expressions in the numerator and/or denominator
Comple fraction: - a fraction which has rational epressions in the numerator and/or denominator o 2 2 4 y 2 + y 2 y 2 2 Steps for Simplifying Comple Fractions. simplify the numerator and/or the denominator
More informationEby, MATH 0310 Spring 2017 Page 53. Parentheses are IMPORTANT!! Exponents only change what they! So if a is not inside parentheses, then it
Eby, MATH 010 Spring 017 Page 5 5.1 Eponents Parentheses are IMPORTANT!! Eponents only change what they! So if a is not inside parentheses, then it get raised to the power! Eample 1 4 b) 4 c) 4 ( ) d)
More informationPre-Algebra 8 Notes Exponents and Scientific Notation
Pre-Algebra 8 Notes Eponents and Scientific Notation Rules of Eponents CCSS 8.EE.A.: Know and apply the properties of integer eponents to generate equivalent numerical epressions. Review with students
More informationReview Topics for MATH 1400 Elements of Calculus Table of Contents
Math 1400 - Mano Table of Contents - Review - page 1 of 2 Review Topics for MATH 1400 Elements of Calculus Table of Contents MATH 1400 Elements of Calculus is one of the Marquette Core Courses for Mathematical
More information( 3x. Chapter Review. Review Key Vocabulary. Review Examples and Exercises 6.1 Properties of Square Roots (pp )
6 Chapter Review Review Ke Vocabular closed, p. 266 nth root, p. 278 eponential function, p. 286 eponential growth, p. 296 eponential growth function, p. 296 compound interest, p. 297 Vocabular Help eponential
More information+ = + + = x = + = + = 36x
Ch 5 Alg L Homework Worksheets Computation Worksheet #1: You should be able to do these without a calculator! A) Addition (Subtraction = add the opposite of) B) Multiplication (Division = multipl b the
More informationINTEGER EXPONENTS HOMEWORK. 1. For each of the following, determine the integer value of n that satisfies the equation. The first is done for you.
Name: Date: INTEGER EXPONENTS HOMEWORK Algebra II INTEGER EXPONENTS FLUENCY. For each of the following, determine the integer value of n that satisfies the equation. The first is done for ou. n = 8 n =
More informationAlgebra(2(Honors( Summer(Packet( ( ( Work(on(this(packet(during(the(summer.( ( ( There(will(be(an(in=class(quiz(on(the(material(the(
Algebra((Honors( Summer(Packet( ( ( Work(on(this(packet(during(the(summer.( ( ( There(will(be(an(in=class(quiz(on(the(material(the( first(week(of(school.( ( ( Please(visit(the(CHS(website(to(view(answers(to(
More information8.3 Zero, Negative, and Fractional Exponents
www.ck2.org Chapter 8. Eponents and Polynomials 8.3 Zero, Negative, and Fractional Eponents Learning Objectives Simplify epressions with zero eponents. Simplify epressions with negative eponents. Simplify
More informationUnit 3 NOTES Honors Common Core Math 2 1. Day 1: Properties of Exponents
Unit NOTES Honors Common Core Math Da : Properties of Eponents Warm-Up: Before we begin toda s lesson, how much do ou remember about eponents? Use epanded form to write the rules for the eponents. OBJECTIVE
More informationHigher. Integration 89
hsn.uk.net Higher Mathematics UNIT UTCME Integration Contents Integration 89 Indefinite Integrals 89 Preparing to Integrate 9 Differential Equations 9 Definite Integrals 9 Geometric Interpretation of Integration
More informationUnit 2 Notes Packet on Quadratic Functions and Factoring
Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a
More informationEXPONENT REVIEW!!! Concept Byte (Review): Properties of Exponents. Property of Exponents: Product of Powers. x m x n = x m + n
Algebra B: Chapter 6 Notes 1 EXPONENT REVIEW!!! Concept Byte (Review): Properties of Eponents Recall from Algebra 1, the Properties (Rules) of Eponents. Property of Eponents: Product of Powers m n = m
More informationAlgebra Final Exam Review Packet
Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:
More informationGlossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression
Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important
More informationNorthwest High School s Algebra 2/Honors Algebra 2
Northwest High School s Algebra /Honors Algebra Summer Review Packet 0 DUE Frida, September, 0 Student Name This packet has been designed to help ou review various mathematical topics that will be necessar
More informationSummer Math Packet (revised 2017)
Summer Math Packet (revised 07) In preparation for Honors Math III, we have prepared a packet of concepts that students should know how to do as these concepts have been taught in previous math classes.
More informationAlgebra 2 Honors Summer Packet 2018
Algebra Honors Summer Packet 018 Solving Linear Equations with Fractional Coefficients For these problems, ou should be able to: A) determine the LCD when given two or more fractions B) solve a linear
More informationM098 Carson Elementary and Intermediate Algebra 3e Section 11.3
Objectives. Solve equations by writing them in quadratic form.. Solve equations that are quadratic in form by using substitution. Vocabulary Prior Knowledge Solve rational equations: Clear the fraction.
More informationLESSON 35: EIGENVALUES AND EIGENVECTORS APRIL 21, (1) We might also write v as v. Both notations refer to a vector.
LESSON 5: EIGENVALUES AND EIGENVECTORS APRIL 2, 27 In this contet, a vector is a column matri E Note 2 v 2, v 4 5 6 () We might also write v as v Both notations refer to a vector (2) A vector can be man
More informationMath-2 Lesson 2-4. Radicals
Math- Lesson - Radicals = What number is equivalent to the square root of? Square both sides of the equation ( ) ( ) = = = is an equivalent statement to = 1.7 1.71 1.70 1.701 1.7008... There is no equivalent
More informationCollege Algebra Final, 7/2/10
NAME College Algebra Final, 7//10 1. Factor the polnomial p() = 3 5 13 4 + 13 3 + 9 16 + 4 completel, then sketch a graph of it. Make sure to plot the - and -intercepts. (10 points) Solution: B the rational
More information7-6. nth Roots. Vocabulary. Geometric Sequences in Music. Lesson. Mental Math
Lesson 7-6 nth Roots Vocabular cube root n th root BIG IDEA If is the nth power of, then is an nth root of. Real numbers ma have 0, 1, or 2 real nth roots. Geometric Sequences in Music A piano tuner adjusts
More informationMATH 021 UNIT 1 HOMEWORK ASSIGNMENTS
MATH 01 UNIT 1 HOMEWORK ASSIGNMENTS General Instructions You will notice that most of the homework assignments for a section have more than one part. Usuall, the part (A) questions ask for eplanations,
More information1 Rational Exponents and Radicals
Introductory Algebra Page 1 of 11 1 Rational Eponents and Radicals 1.1 Rules of Eponents The rules for eponents are the same as what you saw earlier. Memorize these rules if you haven t already done so.
More informationAlgebra/Pre-calc Review
Algebra/Pre-calc Review The following pages contain various algebra and pre-calculus topics that are used in the stud of calculus. These pages were designed so that students can refresh their knowledge
More informationLESSON 12.2 LOGS AND THEIR PROPERTIES
LESSON. LOGS AND THEIR PROPERTIES LESSON. LOGS AND THEIR PROPERTIES 5 OVERVIEW Here's what ou'll learn in this lesson: The Logarithm Function a. Converting from eponents to logarithms and from logarithms
More informationPlacement Test. Circle the letter of the correct answer.
Week Unit 0. What is the place value where the numbers differ?,7,7 A ones tens hundreds thousands. 70 A 6,0 6,0,0,0. 7 A 00 909 999 99. Which of the following is equivalent to the product of? A ( ) (0
More informationRAMAPO&INDIAN*HILLS*SCHOOL*DISTRICT*
1 * * Algebra 2 CP Summer Packet RAMAPO&INDIAN*HILLS*SCHOOL*DISTRICT* DearRamapo*IndianHillsStudent: Pleasefindattachedthesummerpacketforourupcomingmathcourse.Thepurposeof thesummerpacketistoprovideouwithanopportunittoreviewprerequisiteskillsand
More informationExponents are a short-hand notation for writing very large or very. small numbers. The exponent gives the number of times that a number
UNIT 3 EXPONENTS Math 11 Unit 3 Introduction p. 1 of 1 A. Algebraic Skills Unit 3 Exponents Introduction Exponents are a short-hand notation for writing ver large or ver small numbers. The exponent gives
More informationAlgebra 1 Skills Needed to be Successful in Algebra 2
Algebra 1 Skills Needed to be Successful in Algebra A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed
More informationSolutions to the Math 1051 Sample Final Exam (from Spring 2003) Page 1
Solutions to the Math 0 Sample Final Eam (from Spring 00) Page Part : Multiple Choice Questions. Here ou work out the problems and then select the answer that matches our answer. No partial credit is given
More informationAlgebra Review C H A P T E R. To solve an algebraic equation with one variable, find the value of the unknown variable.
C H A P T E R 6 Algebra Review This chapter reviews key skills and concepts of algebra that you need to know for the SAT. Throughout the chapter are sample questions in the style of SAT questions. Each
More informationAlgebra 2 CPA Summer Assignment 2018
Algebra CPA Summer Assignment 018 This assignment is designed for ou to practice topics learned in Algebra 1 that will be relevant in the Algebra CPA curriculum. This review is especiall important as ou
More information3.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS
Section. Logarithmic Functions and Their Graphs 7. LOGARITHMIC FUNCTIONS AND THEIR GRAPHS Ariel Skelle/Corbis What ou should learn Recognize and evaluate logarithmic functions with base a. Graph logarithmic
More informationLESSON #24 - POWER FUNCTIONS COMMON CORE ALGEBRA II
1 LESSON #4 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The
More information5.3 Polynomials and Polynomial Functions
70 CHAPTER 5 Eponents, Polnomials, and Polnomial Functions 5. Polnomials and Polnomial Functions S Identif Term, Constant, Polnomial, Monomial, Binomial, Trinomial, and the Degree of a Term and of a Polnomial.
More informationMathematics. Mathematics 2. hsn.uk.net. Higher HSN22000
hsn.uk.net Higher Mathematics UNIT Mathematics HSN000 This document was produced speciall for the HSN.uk.net website, and we require that an copies or derivative works attribute the work to Higher Still
More informationProperties of Limits
33460_003qd //04 :3 PM Page 59 SECTION 3 Evaluating Limits Analticall 59 Section 3 Evaluating Limits Analticall Evaluate a it using properties of its Develop and use a strateg for finding its Evaluate
More informationSect Definitions of a 0 and a n
5 Sect 5. - Definitions of a 0 and a n Concept # Definition of a 0. Let s examine the quotient rule when the powers are equal. Simplify: Ex. 5 5 There are two ways to view this problem. First, any non-zero
More informationAlgebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions.
Algebra II Notes Unit Si: Polnomials Sllabus Objectives: 6. The student will simplif polnomial epressions. Review: Properties of Eponents (Allow students to come up with these on their own.) Let a and
More informationCourse 15 Numbers and Their Properties
Course Numbers and Their Properties KEY Module: Objective: Rules for Eponents and Radicals To practice appling rules for eponents when the eponents are rational numbers Name: Date: Fill in the blanks.
More informationAlgebra 1 Skills Needed for Success in Math
Algebra 1 Skills Needed for Success in Math A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed to simplif
More informationMini Lecture 9.1 Finding Roots
Mini Lecture 9. Finding Roots. Find square roots.. Evaluate models containing square roots.. Use a calculator to find decimal approimations for irrational square roots. 4. Find higher roots. Evaluat. a.
More informationLESSON #48 - INTEGER EXPONENTS COMMON CORE ALGEBRA II
LESSON #8 - INTEGER EXPONENTS COMMON CORE ALGEBRA II We just finished our review of linear functions. Linear functions are those that grow b equal differences for equal intervals. In this unit we will
More informationOne of your primary goals in mathematics should be to become a good problem solver. It helps to approach a problem with a plan.
PROBLEM SOLVING One of our primar goals in mathematics should be to become a good problem solver. It helps to approach a problem with a plan. Step Step Step Step Understand the problem. Read the problem
More informationCitrus Valley High School
Citrus Valle High School Dear Math I Honors Student, Familiarit with pre-high school math concepts is essential for success in the Integrated Math I Honors class. The majorit of the questions in Math I
More informationUnit 12 Study Notes 1 Systems of Equations
You should learn to: Unit Stud Notes Sstems of Equations. Solve sstems of equations b substitution.. Solve sstems of equations b graphing (calculator). 3. Solve sstems of equations b elimination. 4. Solve
More informationAlgebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology.
Sllabus Objectives:.1 The student will graph quadratic functions with and without technolog. Quadratic Function: a function that can be written in the form are real numbers Parabola: the U-shaped graph
More informationChapter 6: Systems of Equations and Inequalities
Chapter 6: Sstems of Equations and Inequalities 6-1: Solving Sstems b Graphing Objectives: Identif solutions of sstems of linear equation in two variables. Solve sstems of linear equation in two variables
More informationReview of Essential Skills and Knowledge
Review of Essential Skills and Knowledge R Eponent Laws...50 R Epanding and Simplifing Polnomial Epressions...5 R 3 Factoring Polnomial Epressions...5 R Working with Rational Epressions...55 R 5 Slope
More informationLesson 2. When the exponent is a positive integer, exponential notation is a concise way of writing the product of repeated factors.
Review of Exponential Notation: Lesson 2 - read to the power of, where is the base and is the exponent - if no exponent is denoted, it is understood to be a power of 1 - if no coefficient is denoted, it
More informationMath Review Packet #5 Algebra II (Part 2) Notes
SCIE 0, Spring 0 Miller Math Review Packet #5 Algebra II (Part ) Notes Quadratic Functions (cont.) So far, we have onl looked at quadratic functions in which the term is squared. A more general form of
More informationA. Simplifying Polynomial Expressions
A. Simplifing Polnomial Epressions I. Combining Like Terms - You can add or subtract terms that are considered "like", or terms that have the same variable(s) with the same eponent(s). E. 1: 5-7 + 10 +
More informationf(x) = 2x 2 + 2x - 4
4-1 Graphing Quadratic Functions What You ll Learn Scan the tet under the Now heading. List two things ou will learn about in the lesson. 1. Active Vocabular 2. New Vocabular Label each bo with the terms
More information1. Write three things you already know about expressions. Share your work with a classmate. Did your classmate understand what you wrote?
LESSON 1: RATIONAL EXPONENTS 1. Write three things you already know about epressions. Share your work with a classmate. Did your classmate understand what you wrote?. Write your wonderings about working
More informationNAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4
Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as
More informationAlgebra I Notes Concept 00b: Review Properties of Integer Exponents
Algera I Notes Concept 00: Review Properties of Integer Eponents In Algera I, a review of properties of integer eponents may e required. Students egin their eploration of power under the Common Core in
More informationWhich of the following expressions are monomials?
9 1 Stud Guide Pages 382 387 Polnomials The epressions, 6, 5a 2, and 10cd 3 are eamples of monomials. A monomial is a number, a variable, or a product of numbers and variables. An eponents in a monomial
More informationLesson 3 Algebraic expression: - the result obtained by applying operations (+, -,, ) to a collection of numbers and/or variables o
Lesson 3 Algebraic expression: - the result obtained by applying operations (+, -,, ) to a collection of numbers and/or variables o o ( 1)(9) 3 ( 1) 3 9 1 Evaluate the second expression at the left, if
More informationMath-1010 Lesson 4-2. Add and Subtract Rational Expressions
Math-00 Lesson - Add and Subtract Rational Epressions What are like terms? Like variables: Like powers: y y Multiples of the same variable same base and same eponent. Like radicals: same radicand and same
More informationGraphing Inequalities
10 Graphg Inequalities In this chapter, ou will practice graphg equalities that have one or two variables. When there is onl one variable, ou use a number le. When there are two variables, ou use a coordate
More informationDefine a rational expression: a quotient of two polynomials. ..( 3 10) (3 2) Rational expressions have the same properties as rational numbers:
1 UNIT 7 RATIONAL EXPRESSIONS & EQUATIONS Simplifying Rational Epressions Define a rational epression: a quotient of two polynomials. A rational epression always indicates division EX: 10 means..( 10)
More informationACCUPLACER MATH 0310
The University of Teas at El Paso Tutoring and Learning Center ACCUPLACER MATH 00 http://www.academics.utep.edu/tlc MATH 00 Page Linear Equations Linear Equations Eercises 5 Linear Equations Answer to
More informationMATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED
FOM 11 T GRAPHING LINEAR INEQUALITIES & SET NOTATION - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) INEQUALITY = a mathematical statement that contains one of these four inequalit signs: ,.
More informationFOR ALL STUDENTS TAKING ALGEBRA I SUMMER REVIEW PACKET
FOR ALL STUDENTS TAKING ALGEBRA I - SUMMER REVIEW PACKET Dear Student and Parent/Guardian, The math department at Central Dauphin School District wants ou to be successful in Algebra I. We also want ou
More informationChapter 8 Notes SN AA U2C8
Chapter 8 Notes SN AA U2C8 Name Period Section 8-: Eploring Eponential Models Section 8-2: Properties of Eponential Functions In Chapter 7, we used properties of eponents to determine roots and some of
More informationSOLVING SYSTEMS OF EQUATIONS
SOLVING SYSTEMS OF EQUATIONS 4.. 4..4 Students have been solving equations even before Algebra. Now the focus on what a solution means, both algebraicall and graphicall. B understanding the nature of solutions,
More informationProperties of Rational Exponents PROPERTIES OF RATIONAL EXPONENTS AND RADICALS. =, a 0 25 º1/ =, b /3 2. b m
Page of 8. Properties of Rational Eponents What ou should learn GOAL Use properties of rational eponents to evaluate and simplif epressions. GOAL Use properties of rational eponents to solve real-life
More informationSOLVING SYSTEMS OF EQUATIONS
SOLVING SYSTEMS OF EQUATIONS 3.. 3..4 In this course, one focus is on what a solution means, both algebraicall and graphicall. B understanding the nature of solutions, students are able to solve equations
More informationAlgebra I Notes Unit Nine: Exponential Expressions
Algera I Notes Unit Nine: Eponential Epressions Syllaus Ojectives: 7. The student will determine the value of eponential epressions using a variety of methods. 7. The student will simplify algeraic epressions
More informationALGEBRA 2 NY STATE COMMON CORE
ALGEBRA NY STATE COMMON CORE Kingston High School 017-018 emathinstruction, RED HOOK, NY 1571, 015 Table of Contents U n i t 1 - Foundations of Algebra... 1 U n i t - Linear Functions, Equations, and their
More informationAdding and Subtracting Rational Expressions
Adding and Subtracting Rational Epressions As a review, adding and subtracting fractions requires the fractions to have the same denominator. If they already have the same denominator, combine the numerators
More informationCh 5 Alg 2 L2 Note Sheet Key Do Activity 1 on your Ch 5 Activity Sheet.
Ch Alg L Note Sheet Ke Do Activit 1 on our Ch Activit Sheet. Chapter : Quadratic Equations and Functions.1 Modeling Data With Quadratic Functions You had three forms for linear equations, ou will have
More informationCoached Instruction Supplement
Practice Coach PLUS Coached Instruction Supplement Mathematics 8 Practice Coach PLUS, Coached Instruction Supplement, Mathematics, Grade 8 679NASP Triumph Learning Triumph Learning, LLC. All rights reserved.
More information5.6 RATIOnAl FUnCTIOnS. Using Arrow notation. learning ObjeCTIveS
CHAPTER PolNomiAl ANd rational functions learning ObjeCTIveS In this section, ou will: Use arrow notation. Solve applied problems involving rational functions. Find the domains of rational functions. Identif
More informationCh. 7.1 Polynomial Degree & Finite Differences
Ch. 7.1 Polynomial Degree & Finite Differences Learning Intentions: Define terminology associated with polynomials: term, monomial, binomial & trinomial. Use the finite differences method to determine
More informationReteaching (continued)
Zero and Negative Eponents Eercises Write each epression as an integer, a simple fraction, or an epression that contains onl positive eponents. Simplif...3 0. 0-0,000 3. a -5. 3.7 0 a 5 5. 9-6. 3-3 9 p
More informationRELATIONS AND FUNCTIONS through
RELATIONS AND FUNCTIONS 11.1.2 through 11.1. Relations and Functions establish a correspondence between the input values (usuall ) and the output values (usuall ) according to the particular relation or
More informationPolynomial and Rational Functions
Name Date Chapter Polnomial and Rational Functions Section.1 Quadratic Functions Objective: In this lesson ou learned how to sketch and analze graphs of quadratic functions. Important Vocabular Define
More information) approaches e
COMMON CORE Learning Standards HSF-IF.C.7e HSF-LE.B.5. USING TOOLS STRATEGICALLY To be proficient in math, ou need to use technological tools to eplore and deepen our understanding of concepts. The Natural
More informationHow can you write an equation of a line when you are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines
.7 Writing Equations in Point-Slope Form How can ou write an equation of a line when ou are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines Work with a partner. Sketch the
More informationLESSON #28 - POWER FUNCTIONS COMMON CORE ALGEBRA II
1 LESSON #8 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The
More informationSupplemental Worksheet Problems To Accompany: The Algebra 2 Tutor Section 13 Fractional Exponents
Section Fractional Eponents Supplemental Worksheet Problems To Accompany: The Algebra 2 Tutor Section Fractional Eponents Please watch Section of this DVD before working these problems. The DVD is located
More informationSection 1.3 Review of Complex Numbers
1 Section 1. Review of Complex Numbers Objective 1: Imaginary and Complex Numbers In Science and Engineering, such quantities like the 5 occur all the time. So, we need to develop a number system that
More informationEvaluate nth Roots and Use Rational Exponents. p Evaluate nth roots and study rational exponents. VOCABULARY. Index of a radical
. Georgia Performance Standard(s) MMA2a, MMA2b, MMAd Your Notes Evaluate nth Roots and Use Rational Eponents Goal VOCABULARY nth root of a p Evaluate nth roots and stud rational eponents. Inde of a radical
More informationALGEBRAIC EXPRESSIONS AND POLYNOMIALS
MODULE - ic Epressions and Polynomials ALGEBRAIC EXPRESSIONS AND POLYNOMIALS So far, you had been using arithmetical numbers, which included natural numbers, whole numbers, fractional numbers, etc. and
More informationMI-2 Prob. Set #4 DUE: Tuesday, Feb 15, 2011 Spring 11. 4) Write a matrix equation and give result:
MI- Prob. Set #4 DUE: Tuesda, Feb 1, 011 Spring 11 1) Dr. Condie has sport coats, pairs of slacks, 4 shirts and 6 ties that he can choose to wear on an da. a) How man combinations of these four pieces
More informationName Date. and y = 5.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationRadical Expressions and Functions What is a square root of 25? How many square roots does 25 have? Do the following square roots exist?
Topic 4 1 Radical Epressions and Functions What is a square root of 25? How many square roots does 25 have? Do the following square roots eist? 4 4 Definition: X is a square root of a if X² = a. 0 Symbolically,
More informationFINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name
FINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name 1) Find the SUM of the solutions of the equation. 82 + 0 = 16 Use the quadratic formula to solve the equation. (All solutions are real numbers.)
More informationUnit 2: Rational Expressions
Rational Epressions Pure Math 0 Notes Unit : Rational Epressions -: Simplifing Rational Epressions Rational Epressions: - fractions with polnomials as numerator and / or denominator. To Simplif (Reduce)
More informationUse Properties of Exponents
4. Georgia Performance Standard(s) MMAa Your Notes Use Properties of Eponents Goal p Simplif epressions involving powers. VOCABULARY Scientific notation PROPERTIES OF EXPONENTS Let a and b be real numbers
More information2.8 Implicit Differentiation
.8 Implicit Differentiation Section.8 Notes Page 1 Before I tell ou what implicit differentiation is, let s start with an example: EXAMPLE: Find if x. This question is asking us to find the derivative
More information10.3 Solving Nonlinear Systems of Equations
60 CHAPTER 0 Conic Sections Identif whether each equation, when graphed, will be a parabola, circle, ellipse, or hperbola. Then graph each equation.. - 7 + - =. = +. = + + 6. + 9 =. 9-9 = 6. 6 - = 7. 6
More informationLESSON #1 - BASIC ALGEBRAIC PROPERTIES COMMON CORE ALGEBRA II
1 LESSON #1 - BASIC ALGEBRAIC PROPERTIES COMMON CORE ALGEBRA II Mathematics has developed a language all to itself in order to clarif concepts and remove ambiguit from the analsis of problems. To achieve
More informationWe have examined power functions like f (x) = x 2. Interchanging x
CHAPTER 5 Eponential and Logarithmic Functions We have eamined power functions like f =. Interchanging and ields a different function f =. This new function is radicall different from a power function
More information