# Algebra 2

In: Other Topics

Submitted By Aurorabosse
Words 605
Pages 3
Algebra 2

Lesson 5-5

Example 1 Equation with Rational Roots
Solve 2x2 – 36x + 162 = 32 by using the Square Root Property.

2x2 – 36x + 162 = 32 Original equation
2(x2 – 18x + 81) = 2(16) Factor out the GCF. x2 – 18x + 81 = 16 Divide each side by 2. (x – 9)2 = 16 Factor the perfect trinomial square. x – 9 = Square Root Property x – 9 = ±4 = 4 x = 9 ± 4 Add 9 to each side. x = 9 + 4 or x = 9 – 4 Write as two equations. x = 13 x = 5 Solve each equation.

The solution set is {5, 13}. You can check this result by using factoring to solve the original equation.

Example 2 Equation with Irrational Roots
Solve x2 + 10x + 25 = 108 by using the Square Root Property.

x2 + 10x + 25 = 108 Original equation (x + 5)2 = 108 Factor the perfect square trinomial. x + 5 = Square Root Property x = –5 ±6 Add –5 to each side; = 6 x = –5 + 6 or x = –5 – 6 Write as two equations. x ≈ 5.4 x ≈ –15.4 Use a calculator.

The exact solutions of this equation are –5 – 6 and –5 + 6. The approximate solutions are –15.4 and 5.4. Check these results by finding and graphing the related quadratic function.

x2 + 10x + 25 = 108 Original equation x2 + 10x – 83 = 0 Subtract 108 from each side. y = x2 + 10x – 83 Related quadratic function.

CHECK Use the ZERO function of a graphing calculator. The approximate zeros of the related function are –15.4 and 5.4.

Example 3 Complete the Square
Find the value of c that makes x2 –x + c a perfect square. Then write the trinomial as a perfect square.
Step 1|Find one half of.|• = |
|||
Step 2|Square the result of Step 1|= |
Step 3|Add the result of Step 2 to x2 –x|x2 –x + |
The trinomial x2 –x + can be written as.

Example 4 Solve an Equation by...

### Similar Documents

#### Term Paper

...Algebra 1: Simplifying Algebraic Expressions Lesson Plan for week 2 Age/Grade level: 9th grade Algebra 1 # of students: 26 Subject: Algebra Major content: Algebraic Expressions Lesson Length: 2 periods of 45 min. each Unit Title: Simplifying Algebraic Expressions using addition, subtraction, multiplication, and division of terms. Lesson #: Algebra1, Week 2 Context This lesson is an introduction to Algebra and its basic concepts. It introduces the familiar arithmetic operators of addition, subtraction, multiplication, and division in the formal context of Algebra. This lesson includes the simplification of monomial and polynomial expressions using the arithmetic operators. Because the computational methods of variable quantities follows from the computational methods of numeric quantities, then it should follow from an understanding of basic mathematical terminology including the arithmetic operators, fractions, radicals, exponents, absolute value, etc., which will be practiced extensively prior to this lesson. Objectives • Students will be able to identify basic algebraic concepts including: terms, expressions, monomial, polynomial, variable, evaluate, factor, product, quotient, etc. • Students will be able to simplify algebraic expressions using the four arithmetic operators. • Students will be able to construct and simplify algebraic expressions from given parameters. • Students will be able to evaluate algebraic......

Words: 692 - Pages: 3

#### Math Used in the Paralegal Profession

...MM150 Prof. Mowen May 21, 2011 INTRODUCTION This paper is on what kind of math I will be using in my chosen profession. My chosen profession is the paralegal profession. I know that I will not need to know a lot of math for this profession. As a paralegal professional I will be using math every day. I will be using math for everything from keeping track of billable hours to estimating damages in a lawsuit. I will need to know basic math, basic algebra, and first year algebra. Basic math and basic algebra consists of addition, subtraction, multiplication, fractions, decimals, percentages, and negative numbers (www.xpmath.com). First year algebra consists of using formulas (www.xpmath.com). In this paper I will explain in detail the math that I would use in the four different types of law offices for a paralegal professional that I am interested in. These types of law offices are family law, civil litigation, probate and estate law, and criminal law. Family Law In a family law office I would use basic math and first year algebra. I would be using addition, subtraction, multiplication, division, and a formula set by the courts to calculate child support and spousal support payments. I also would be using addition, subtraction, multiplication, and division to figure out how much the marital property is worth and how much each party would get if the clients decide to sell the property and split the value of the property. I would also use addition and multiplication to......

Words: 493 - Pages: 2

Free Essay

#### Parabola Investigation

...and y=2x, then I will prove my conjectures and to broaden the scope of the investigation to include other lines and other types of polynomials. 1. Consider the parabola y=(x-3)2 +2=x2-6x+11 and the lines y=x and y=2x. The original graph is shown below (graph 1.1) Find the intersections of the parabola with y=x and y=2x, Graph 1.2. Also, label the x-values of the intersections with the line y=x as they appear from left to right on the x-axis as a1 and a2; label the x-values of the intersections with the line y=2x as b1 and b2. Now, I will using the graph and graph calculator, find the values of a1-b1 and b2-a2 and name them respectively SL and SR. SL=a1-b1=2.381966-1.763932=0.618034 SR=b2-a2=6.236068-4.618034=1.618034 Now, calculate the quantity D= │SL-SR│ D= │SL-SR│=│0.618034-1.618034│=1 By algebra calculation, D=│SL-SR│ =│ a1-b1-(b2-a2) │ =│ a1-b1-b2+a2 │ =│ (a1+ a2 )-(b1+b2) │ Now, I will try other parabolas of the form y=ax2+bx+c, a＞0, with vertices in quadrant 1, intersected by the lines y=x and y=2x. y=x2+2x+1 [pic] From the graph we can see there is no intersection of the parabola and y=x, y=2x. Using the algebra way: Solve: (a) x2+2x+1=x (b) x2+2x+1=2x (a) x2+2x+1=x x2+x+1=0 [pic] X=[pic] a1+a2= 1 (b)......

Words: 566 - Pages: 3

Free Essay

#### Title

...this year has been teaching most of the 2012 class algebra 2. The way he handles things may seem harsh at times but inevitably will only lead to our success in life. My first year having Dr. Beach was my sophomore year geometry class. I was so use to flying by all my classes with hardly looking into my notes and homework when Dr. Beaches class started to demand more from us. It started with more homework, a lot of random projects and of course our financial/intelligent conversations. There are many good sides to his class. Some things would be the lessons you learn. He teaches us that we are responsible for our actions and he doesn’t fail us, we only fail ourselves. We basically write out our own grades by deciding to do the homework, extra credit, study for quizzes/tests and taking good notes. Taking responsibility is a HUGE theme in our algebra 2 class this year especially. I feel like everything in Dr. Beach’s class has had a separate meaning then just algebra 2 or geometry. All the home work we receive is just to prepare us for the amount of work in college and our future jobs. The quizzes and tests are preparing us for the responsibilities of using our skills and abilities then turning them into something greater. The lessons are to help us comprehend and understand complex and even basic things. Some negative sides to Dr. Beach’s methods would be the feeling that algebra 2 is our only class and keeping up with homework,......

Words: 674 - Pages: 3

Free Essay

#### Resume

...[pic] Aguirre, Jedidiah Joel C. 55 Doña Feliza Subd. Brgy Paciano, Calamba City Mobile Number: 0926-7368277 Email Ad: jed_aguirre@yahoo.com Objectives To acquire an exciting and challenging job as Mathematics High School Tutor. Experiences 3rd Year High School : Quarterly Remedial Class Instructor in Mathematics 3 (Geometry) : Personal Tutorial Sessions for Mathematics 2 (Intermediate Algebra) 4th Year High School : Quarterly Remedial Class Instructor in Mathematics 4 (Advanced Algebra and Trigonometry) Summer, 2009 :Personal Tutorial Sessions for Math-UPCAT. 2nd Semester, 2010 :Literacy Training Service 2: Kalayaan Elementary School Grade 6 Mathematics Teacher 1st Semester, 2011 :Tutor in Princeton Academy, BelAir, Sta. Rosa, Laguna 2nd Semester, 2011 : Student-instructor in UPLB Math Division’s Think Tank Toe Achievements Elementary School : 3rd Place: Metrobank-MTAP-DepEd NCR Math Challenge Sectoral Level 10th Place: Metrobank-MTAP-DepEd NCR Math Challenge Regional Level Best in Math, Valedictorian High School : Best in Math (3rd Year and 4th Year), Best in Physics (4th year), 1st place, 2008 Math Masters, Meycauayan College. College 1st Semester, AY 08-09 : 4th Placer, UPLB Math Wizard College Scholar 2nd Semester, AY 08-09 : Participant, 36th Annual Nationwide Search......

Words: 367 - Pages: 2

Free Essay

#### The Implication of Technology Remediation in Academic Performance of Student

...Detailed Lesson Plan in Algebra Feb. 11, 2015 I. Objectives a. Define polynomials b. Classify polynomials according to number c. Perform operation involving polynomials, addition and subtraction. II. Subject Matter Topic: Polynomials Materials: visuals, chalk and board Reference/s: College Algebra, pages 1-4 III. Presentation A. Preliminaries 1. Opening prayer 2. Checking of Attendance 3. Checking of Assignments 4. Motivation (Video clip) B. Lesson Proper Teacher’s Activity In the video that you’ve watched, what will be our lesson for today? Yes, George? Yes it has. Anyone can tell what it is? Yes, Fred. Very good. Can someone tell what is a polynomial is? Yes Claire. Yes, very well said, any additional information? Ok, so let’s proceed. So terms that different only in their constant coefficients are called “like terms”. Polynomials and algebraic expressions can be classified(according to the number of term) as; Monomial – having one term Binomial – having two terms Trinomials – having three termsMultinomials – having more than three terms. The degree of a polyomial is determined by the hiegst exponent of its variable. Someone give me an examples of polynomials. (called several students). Thank you for your answers. Is there any question? Oko next is adding and subtracting polynomials: Rule:Add/subtract the constant......

Words: 483 - Pages: 2

#### Mathematics and Management

...LONDON'S GLOBAL UNIVERSITY Mathematics with Management Studies BSc UCAS code: G1N2 www.ucl.ac.uk/prospectus/maths MATHEMATICS WITH MANAGEMENT STUDIES BSc This BSc combines a broad-based training in mathematics with highly practical courses from UCL’s Department of Management Science and Innovation, which will be of direct use to those seeking a career in management. No previous knowledge of management studies is required. Degree summary • • • • Gain transferable skills such as numeracy, problem-solving and logical thinking, which can lead to a large variety of interesting, diverse and well-paid careers. All of the courses given by UCL's Department of Management Science are validated by external experts from the private, public and charitable sectors. Many of our graduates choose to build their management knowledge and experience by following a further management qualification, such as the MBA (Masters in Business Administration). UCL's internationally renowned Mathematics Department is home to world-leading researchers in a wide range of fields, especially geometry, spectral theory, number theory, fluid dynamics and mathematical modelling. Peer Assisted Learning has been pioneered in the department, with second-year students offering support and advice to first years. Your career We aim to develop your skills in mathematical reasoning, problem-solving and accurate mathematical manipulation. You will also learn to handle abstract concepts and to think......

Words: 1320 - Pages: 6

Free Essay

#### Mat 222 Week 3 Assignment Real World Radical Formulas

...This file MAT 222 Week 3 Assignment Real World Radical Formulas contains solutions to the following tasks: 1.103. Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2 (www.sailing.com). For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function. a).Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet. b). Solve the equation for d. 2.104. Sailboat speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a displacement of d pounds and a sail area of A square feet S is determined by the function a)Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds. b) Write d in terms of A and S. Mathematics - Algebra Real World Radical Formulas . Read the following instructions in order to complete this assignment: a. Solve parts a and b of problem 103 on page 605 and problem 104 on page 606 of Elementary and Intermediate Algebra . b. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include: § An explanation of what the parts of the formula mean before using it to get your answers. Study......

Words: 403 - Pages: 2

Free Essay

#### Algebra Assignment

...Many people are intimidated and afraid of mathematics and algebra largely due to the fact that upon first glance, certain problems or expressions may seem overwhelmingly large, difficult, or complicated. Along with remembering formulas, this can often times lead to anger, confusion, and frustration. There are several very important key elements and aspects involved within mathematics that helps combat this confusion and frustration and can even help the most intimidated person feel at ease and comfortable with solving these problems. This particular report will demonstrate the importance of understanding certain key mathematical principles and components and show how understanding and utilizing certain mathematical definitions can help limit the amount of confusion and intimidation one may have. These definitions include but are not limited to simplifying, adding like terms, coefficient, distributive property, and removing parenthesis. This report will also demonstrate how much easier and more simplistic mathematics and algebra can be by remembering and utilizing just a few important concepts. Example 1: 2^a(a-5) +4(a-5) This is the first example that will be used. The variable a is used. This particular example has a coefficient of two. Step 1: The distributive property can be utilized to multiply 2a by everything inside of the parenthesis (a-5 in this case) resulting in: 2a^2-10a Step 2: The distributive property is used once again to multiply 4 by everything in......

Words: 645 - Pages: 3

Free Essay

#### Miss

...06 Section 6 pp058-067.qxd 6.1 26/8/03 10:04 am Page 58 Key words Collecting like terms like terms unknown Understand which terms you can add together and which you cannot 3 ϩ 3 is two lots of 3 so 3 ϩ 3 ϭ 2 ϫ 3 a ϩ a is two lots of a so a ϩ a ϭ 2 ϫ a We write 2 ϫ a as 2a. Just as 2 ϫ 3 and 4 ϫ 3 can be added together to give 6 ϫ 3, 2a and 4a can be added together to give 6a. These terms are called like terms because they contain the same letter. Like terms can be added together – this is called collecting like terms. Instead of writing 2m ϩ 3m ϩ b ϩ 2b, we can write 5m ϩ 3b or 3b ϩ 5m. We cannot combine 5m and 3b in any simpler way than this because m and b are not like terms – they stand in for different unknown numbers. We can multiply two or more unknowns together. a ϫ b is written as ab. b ϫ a is the same as a ϫ b and is also written as ab. Instead of writing 2a ϩ 3b ϩ 3ab ϩ ba, we can write 2a ϩ 3b ϩ 4ab. We can add 3ab to ba to make 4ab because ab and ba are like terms. Example Simplify the following by collecting like terms: a) 3m ϩ 4m ϩ m ϩ n ϩ 2n b) 4mv ϩ 2z Ϫ 3mv ϩ z ϩ 3m There are eight lots of m and three lots of n. a) 3m ϩ 4m ϩ m ϩ n ϩ 2n ϭ 8m ؉ 3n b) 4mv ϩ 2z Ϫ 3mv ϩ z ϩ 3m ϭ mv ϩ 3z ϩ 3m First look at the mv terms: 4mv Ϫ 3mv ϭ 1mv (which we usually write as mv) Now look at the z terms: 2z ϩ z ϭ 3z Now look at the m terms: you have 3m Exercise 6.1 ......................................................

Words: 4206 - Pages: 17

Free Essay

#### Algerbra

Words: 509 - Pages: 3

#### Discussion Question

Words: 852 - Pages: 4

#### Higher Order

...Thinking and Diverse Learners Grand Canyon University: Secondary Methods and Data-Driven Pedagogy April Smith GCU: SED-444 August 25, 2013 Higher Order Thinking and Diverse Learners This unit is designed for students in beginning Algebra classes. It is an introduction to the basic functions of algebra including the definition of an equation, using basic mathematical skills to solve equations, and applying equations to problem solving. South Carolina Standard 8-3: Through the process standards students will demonstrate an understanding of equations, inequalities, and linear functions (South Carolina Department of Education, 2007). Specific Indicators as outlined by the South Carolina Department of Education 8-3.1 Translate among verbal, graphical, tabular and algebraic representations of linear functions. 8-3.2 Represent algebraic relationships with equations and inequalities. 8-3.3 Use properties to examine equivalence of a variety of algebraic expressions. 8-3.4 Apply procedures to solve multi-step equations. 8-3.5 Classify relationships between two variables as linear or non-linear. Objectives Day 1 Objective: Students will learn the definition of an algebraic equation and the parts of an equation. Day 2 Objective: Students will apply their knowledge of addition and subtraction to solve algebraic equations. Day 3 Objective: Students will demonstrate proficiency in applying multiplication and division to solving algebraic equations.......

Words: 1259 - Pages: 6

Free Essay

#### Love

...Distinguished Honors student, Key Award Student (most respectable and distinguished students), and a member of the National Honors Society in Simon Gratz Mastery Charter. I rank one of the highest currently and have remained one of the highest since 9th grade. I am very self driven, active, and a goal achiever. My patients, positivity, and ability to connect with others makes me more eligible to participate in my community and help provide a safe environment. EDUCATION Simon Gratz Mastery Charter HighSchool, Philadelphia, PA - 08/2011 to Present GPA Weighted: 4.07 GPA Unweighted: 3.95 * Competed Coursework In : Literature 9, Algebra 1, Physical Science, Sophomore Seminar, Composition, and African American History (9th grade). Biology, Geometry, Internship, Literature 10, World History, and Mastery Class (10 grade), AP Literature, AP U.S history, Algebra 2, Chemistry, and Spanish 1(11th Grade) * Currently Enrolled In: AP Literature, AP Government, AP Biology, Senior Seminar, Physical Ed., Spanish 11, and Pre-Calculus STRENGTHS / WEAKNESSES: * Strengths: Easily establishes friends, gets along well with peers, accepts responsibility well, study and work skills are strong, initiates interactions with peers, appropriately assertive, grade appropriate grammar, likes to get involved, strong decision making skills, strong ability to manage behavior, strong organization skills * Weaknesses: Difficulty to speaking amongst big crowds * How Am I......

Words: 315 - Pages: 2

Free Essay

#### Dominans of Rational Expression

...and remain a real number. The first letter of my names starts with a "T" so these are the rational expressions that I'll be solving: 1 - x^2                                    and                                             2b - 2          x                                                                                             2b^2- 8 1 - x^2                                                     This is the first given expression. Since we know that denominator is the valuable, x can not equal zero be because it will make the expression undefined, but any                                        x                                                         other real number will solve the expression.       x = 0                                                        The zero is the excluded value.   We can see that the domain for this expression is a set of all  real numbers where zero is excluded from the value. The expression is written like this:D = {x| x € R b ≠ 0}. For the second expression, I'll have to set the denominator equal to zero the find the excluded values.    2b - 2                                                   Again, this is the given expression. In order for me to find the excluded values, I'll have to factor the denominator and make them equal to zero in order to solve for b. 2b^2 - 8 2b - 2...

Words: 496 - Pages: 2