Original site. translation. transformation. Decide whether the red figure is a translation of the blue figure. Compare a Figure and Its Image
|
|
- Phebe Shelton
- 6 years ago
- Views:
Transcription
1 Page of Translations Goal Identif and use translations. Ke Words translation image transformation In 996, New York Cit s Empire Theater was slid 70 feet up 2nd Street to a new location. Original site A slide is also called a translation. The new figure after the translation is the image. In this book, the original figure is given in blue and its image in red, as shown at the right. Translation Image A translation is one kind of transformation. A transformation is an operation that maps, or moves, a figure onto an image. You will stud other transformations in Lessons 5.7, 7.6, and.8. Student Help VOCAULARY TIP Use the following relationship to help ou remember that a translation is a slide: translation slide EXAMPLE Compare a Figure and Its Image Decide whether the red figure is a translation of the blue figure. a. b. c. Solution a. Yes, this is a translation. b. No, this is not a translation. The image is a mirror image of the original figure. c. No, this is not a translation. The original figure is rotated. Compare a Figure and Its Image Decide whether the red figure is a translation of the blue figure Chapter 3 Parallel and Perpendicular Lines
2 Page 2 of 8 Student Help READING TIP In the diagram at the right, A is read as A prime. Labeling Translations When labeling points on the image, write the prime smbol ( ) net to the letter used in the original figure, as shown at the right. A In a translation, segments connecting points Image in the original figure to their corresponding points in the image are congruent and parallel. For eample, AA &** and &* at the right are congruent and parallel. A EXAMPLE 2 Describe Translations Describe the translation of the segment. Solution Point P is moved units to the right and 2 units down to get to point P. So, ever point on PQ &* moves units to the right and 2 units down. P(2, ) Œ(, 2) 2 P (6, 2) Œ (5, 0) Translations in a coordinate plane can also be described using the following coordinate notation: (, ) ( a, b) Each point shifts a units horizontall (right or left) and b units verticall (up or down). When moving right or up, add the number of units. When moving left or down, subtract the number of units. Here are some eamples: (, ) (, ) (, ) (, ) IStudent Help I C L A S S Z O N E. C O M MORE EXAMPLES More eamples at classzone.com EXAMPLE Describe the translation using coordinate notation. Solution 3 Use Coordinate Notation Each point is moved 3 units to the left and units up. ANSWER The translation can be described using the notation (, ) ( 3, ) Translations 53
3 Page 3 of 8 Describe Translations Describe the translation using words and coordinate notation EXAMPLE Draw Translated Figures Student Help Draw the triangle given b points A( 2, 5), (0, 7), and C(3, 7). Then draw the image of the triangle after the translation given b (, ) ( 2, 3). READING TIP In this book, shapes are named b listing in order the labels at their corners. For eample, the blue triangle in Eample is named T AC. Solution First, sketch T AC as shown. To find points A,, and C, start at points A,, and C, and slide each point 2 units to the right and 3 units down. T AC T A C A 2 C 3 C A( 2, 5) A (0, 2) (0, 7) (2, ) C(3, 7) C (5, ) A Notice that each -value of T A C is 2 units more than the corresponding -value of T AC and each -value of T A C is 3 units less than the corresponding -value of T AC. Draw Translated Figures Draw the image of the figure after the given translation. 6. (, ) ( 3, 2) 7. (, ) ( 3, ) F G J H W X Z Y 5 Chapter 3 Parallel and Perpendicular Lines
4 Page of Eercises Guided Practice Vocabular Check. What is a translation? 2. Complete the statement: A translation shows a blue triangle and a red triangle. The blue triangle is the original figure and the red triangle is the?. Skill Check Window Frames Decide whether opening the window is a translation of the moving part. 3. Double hung. Casement 5. Sliding Decide whether the statement is true or false. Eplain. 6. The red figure is a translation of the blue figure. 7. To move from T AC to T A C, shift 3 units to the right and 2 units up. 8. The translation from T AC to T A C is given b (, ) ( 3, 2). C A C A Practice and Applications Etra Practice See p Compare a Figure and Its Image Decide whether the red figure is a translation of the blue figure Homework Help Eample : Es. 9 Eample 2: Es. 5 2 Eample 3: Es. 22, 23 Eample : Es Translations 55
5 Page 5 of 8 Matching Translations Match the description of the translation with its diagram. 5. units right and 3 units up 6. 6 units right and 2 units down 7. 7 units left and unit up 8. 5 units right and 2 units down A.. C. D. Describing Translations Describe the translation using words Coordinate Notation Describe the translation using coordinate notation A Point and Its Image Find the image of the point using the translation (, ) (, 3). 2. (2, 5) 25. ( 3, 7) 26. (, ) 27. (, 6) 28. (0, 0) 29. (, 3) 30. (3, ) 3. (, ) 56 Chapter 3 Parallel and Perpendicular Lines
6 Page 6 of 8 Finding an Image Find the coordinates of P, Q, R, and S using the given translation. 32. (, ) (, ) Œ 33. (, ) ( 3, 2) 3 R 3. (, ) ( 5, 5) P Chess CHESS TEAMS The chess team at the Universit of Marland, altimore Count (UMC), has become a strong, nationall recognized team. This is due in part to the efforts of UMC President Dr. Freeman A. Hrabowski, III (second from the left). 35. (, ) (, 3) Chess In chess, si different kinds of pieces are moved according to individual rules. The board below shows some moves for the Knight (the piece shaped like a horse). 36. Describe the translation used b the White Knight to capture the lack Pawn. 37. Assume that the White Knight has taken the place of the lack Pawn. Describe the translation used b the lack Knight to move to capture the White Knight at its new location. Drawing Translated Figures Draw the image of the figure after the given translation. 38. (, ) ( 2, ) 39. (, ) (, 5) F S E. 37 E. 36 A C H G 0. (, ) ( 5, 3). (, ) ( 3, 8) Q P W 2 X S R Z Y Use Points on an Image A point on an image and the translation are given. Find the corresponding point on the original figure. 2. Point on image: (0, 3); translation: (, ) ( 3, 2) 3. Point on image: ( 2, ); translation: (, ) ( 5, ). Point on image: (6, ); translation: (, ) ( 3, 7) 3.7 Translations 57
7 Page 7 of 8 You be the Judge 5. The figure on the grid shown at the right is the image after the translation (, ) ( 6, ). One of our classmates tells ou that C on the original figure is (2, 2). Do ou agree? Eplain our reasoning. C A Technolog In Eercises 6 and 7, use geometr software to complete the steps below. Draw a triangle and translate it. 2 Construct &* JJ and KK &**. 6. If two lines have the same slope, then the are parallel. Measure the slopes of &* JJ and KK &**. Are&* JJ and KK &** parallel? 7. What should makjj mak KJ be? Measure the angles and check our answer. J K L J K L Standardized Test Practice Mied Review 8. Challenge Point C is located at (, 3). The translation that shifts C to C is given b (, ) ( 5, ). The translation that shifts C to C is given b (, ) (, 8). Give the coordinate notation that describes the translation directl from C to C. (Hint: Start b plotting C, C, and C.) Multiple Choice In Eercises 9 and 50, use the diagram below. 9. Find the coordinates of T using the translation (, ) ( 5, 2). A (3, 7) (0, 0) C (3, 5) D ( 5, 7) 50. Find the coordinates of W using the translation (, ) ( 3, 3). F (5, ) G (, 7) H (5, 7) J (, ) Classifing Angles State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure. (Lesson.6) W V T U A C F G H Y X Z 58 Chapter 3 Parallel and Perpendicular Lines
8 Page 8 of 8 Algebra Skills Problem Solving Use problem solving strategies to answer the question. (Skills Review, p. 653) 5. Your telephone compan charges $.5 per minute for all long distance calls. This month ou paid $2.60 for long distance calls. How man minutes did ou spend on long distance calls? 55. You just bought a CD single that has four tracks. In how man different orders can the songs be plaed? Ordering Numbers Write the numbers in order from least to greatest. (Skills Review, p. 662) , 0.5, 0,.0, 0., ,.2, 0.7,.5, 0,., , 7.6, 0.77, 6.6, 0.7, , 6.3, 6.8, 6., 6, 6.09 Quiz 3 Determine whether enough information is given to conclude that m n. Eplain. (Lesson 3.5). 2. m n 3. m n m n In Eercises 6, eplain how ou would show that p q. State an theorems or postulates that ou would use. (Lesson 3.6). p q 5. p n q 6. n q p n Draw a vertical line l and construct a line m perpendicular to it through a point P to the left of line l. (Lesson 3.6) In Eercises 8 and 9, describe the translation of the figure using coordinate notation. (Lesson 3.7) Translations 59
Words Algebra Graph. 5 rise } run. } x2 2 x 1. m 5 y 2 2 y 1. slope. Find slope in real life
TEKS 2.2 a.1, a.4, a.5 Find Slope and Rate of Change Before You graphed linear functions. Now You will find slopes of lines and rates of change. Wh? So ou can model growth rates, as in E. 46. Ke Vocabular
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 informationReady To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities
A Read To Go n? Skills Intervention -1 Solving Linear Equations and Inequalities Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular equation solution of an equation linear
More informationMaintaining Mathematical Proficiency
Name Date Chapter 3 Maintaining Mathematical Proficienc Plot the point in a coordinate plane. Describe the location of the point. 1. A( 3, 1). B (, ) 3. C ( 1, 0). D ( 5, ) 5. Plot the point that is on
More informationSolving Systems of Linear Equations by Graphing
. Solving Sstems of Linear Equations b Graphing How can ou solve a sstem of linear equations? ACTIVITY: Writing a Sstem of Linear Equations Work with a partner. Your famil starts a bed-and-breakfast. The
More informationGraph Quadratic Functions in Standard Form
TEKS 4. 2A.4.A, 2A.4.B, 2A.6.B, 2A.8.A Graph Quadratic Functions in Standard Form Before You graphed linear functions. Now You will graph quadratic functions. Wh? So ou can model sports revenue, as in
More informationStart at the origin. Move left 3 units since the x-coordinate. Start at the origin. Since the x-coordinate is 0, the point
Answers (Lesson -) Lesson - - Stud Guide and Intervention The Coordinate Plane Identif Points In the diagram at the right, points are located in reference to two perpendicular number lines called aes.
More informationSystems of Linear Inequalities
. Sstems of Linear Inequalities sstem of linear inequalities? How can ou sketch the graph of a ACTIVITY: Graphing Linear Inequalities Work with a partner. Match the linear inequalit with its graph. + Inequalit
More information2.1 Evaluate and Graph Polynomial
2. Evaluate and Graph Polnomial Functions Georgia Performance Standard(s) MM3Ab, MM3Ac, MM3Ad Your Notes Goal p Evaluate and graph polnomial functions. VOCABULARY Polnomial Polnomial function Degree of
More informationEvaluate Logarithms and Graph Logarithmic Functions
TEKS 7.4 2A.4.C, 2A..A, 2A..B, 2A..C Before Now Evaluate Logarithms and Graph Logarithmic Functions You evaluated and graphed eponential functions. You will evaluate logarithms and graph logarithmic functions.
More informationSample Problems For Grade 9 Mathematics. Grade. 1. If x 3
Sample roblems For 9 Mathematics DIRECTIONS: This section provides sample mathematics problems for the 9 test forms. These problems are based on material included in the New York Cit curriculum for 8.
More informationSolving Polynomial Equations Exponential Growth in Factored Form
7.5 Solving Polnomial Equations Eponential Growth in Factored Form is written in factored form? How can ou solve a polnomial equation that Two polnomial equations are equivalent when the have the same
More information4.6 Model Direct Variation
4.6 Model Direct Variation Goal p Write and graph direct variation equations. Your Notes VOCABULARY Direct variation Constant of variation Eample Identif direct variation equations Tell whether the equation
More informationLesson Remember. Finding Domain and Range from a Graph EXAMPLE. Key Vocabulary
0. Lesson Ke Vocabular function domain range function form Functions A function is a relationship that pairs each input with eactl one output. The domain is the set of all possible input values. The range
More informationGraph Square Root and Cube Root Functions
TEKS 6.5 2A.4.B, 2A.9.A, 2A.9.B, 2A.9.F Graph Square Root and Cube Root Functions Before You graphed polnomial functions. Now You will graph square root and cube root functions. Wh? So ou can graph the
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 informationΔABC Δ ΔBAC Δ ΔCAB Δ ΔACB Δ ΔBCA Δ ΔCBA Δ
Geometry & Statistics Name: Guided Notes: Triangle Congruence Congruence Reminder: Two geometric figures are if they have exactly the same size and shape. Ex 1: ΔABC ΔPQR. List the corresponding congruent
More informationGraph and Write Equations of Circles
TEKS 9.3 a.5, A.5.B Graph and Write Equations of Circles Before You graphed and wrote equations of parabolas. Now You will graph and write equations of circles. Wh? So ou can model transmission ranges,
More informationProperties of the Graph of a Quadratic Function. has a vertex with an x-coordinate of 2 b } 2a
0.2 Graph 5 a 2 b c Before You graphed simple quadratic functions. Now You will graph general quadratic functions. Wh? So ou can investigate a cable s height, as in Eample 4. Ke Vocabular minimum value
More informationInverse Trigonometric Functions. inverse sine, inverse cosine, and inverse tangent are given below. where tan = a and º π 2 < < π 2 (or º90 < < 90 ).
Page 1 of 7 1. Inverse Trigonometric Functions What ou should learn GOAL 1 Evaluate inverse trigonometric functions. GOAL Use inverse trigonometric functions to solve real-life problems, such as finding
More informationComparing Linear and Nonlinear Functions 5.5. ACTIVITY: Finding Patterns for Similar Figures. How can you recognize when a pattern
5.5 Comparing Linear and Nonlinear Functions in real life is linear or nonlinear? How can ou recognize when a pattern ACTIVITY: Finding Patterns for Similar Figures Work with a partner. Cop and complete
More informationSystems of Linear and Quadratic Equations. Check Skills You ll Need. y x. Solve by Graphing. Solve the following system by graphing.
NY- Learning Standards for Mathematics A.A. Solve a sstem of one linear and one quadratic equation in two variables, where onl factoring is required. A.G.9 Solve sstems of linear and quadratic equations
More information15.2 Graphing Logarithmic
_ - - - - - - Locker LESSON 5. Graphing Logarithmic Functions Teas Math Standards The student is epected to: A.5.A Determine the effects on the ke attributes on the graphs of f () = b and f () = log b
More informationExplore 1 Graphing and Analyzing f(x) = e x. The following table represents the function ƒ (x) = (1 + 1 x) x for several values of x.
1_ 8 6 8 Locker LESSON 13. The Base e Teas Math Standards The student is epected to: A.5.A Determine the effects on the ke attributes of the graphs of ƒ () = b and ƒ () = log b () where b is, 1, and e
More informationThe standard form of the equation of a circle is based on the distance formula. The distance formula, in turn, is based on the Pythagorean Theorem.
Unit, Lesson. Deriving the Equation of a Circle The graph of an equation in and is the set of all points (, ) in a coordinate plane that satisf the equation. Some equations have graphs with precise geometric
More informationTRANSFORMATIONS OF f(x) = x Example 1
TRANSFORMATIONS OF f() = 2 2.1.1 2.1.2 Students investigate the general equation for a famil of quadratic functions, discovering was to shift and change the graphs. Additionall, the learn how to graph
More informationReady To Go On? Skills Intervention 6-1 Polynomials
6A Read To Go On? Skills Intervention 6- Polnomials Find these vocabular words in Lesson 6- and the Multilingual Glossar. Vocabular monomial polnomial degree of a monomial degree of a polnomial leading
More informationAlgebra 1 CP Semester Exam Review
Name: Hr: Algebra CP Semester Eam Review GET ORGANIZED. Successful studing begins with being organized. Bring this packet with ou to class ever da. DO NOT FALL BEHIND. Do the problems that are assigned
More informationReady To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions
Read To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Find these vocabular words in Lesson 5-1 and the Multilingual Glossar. Vocabular quadratic function parabola verte
More informationReady To Go On? Skills Intervention 12-1 Inverse Variation
12A Find this vocabular word in Lesson 12-1 and the Multilingual Glossar. Identifing Inverse Variation Tell whether the relationship is an inverse variation. Eplain. A. Read To Go On? Skills Intervention
More information15.4 Equation of a Circle
Name Class Date 1.4 Equation of a Circle Essential Question: How can ou write the equation of a circle if ou know its radius and the coordinates of its center? Eplore G.1.E Show the equation of a circle
More information9.2. Cartesian Components of Vectors. Introduction. Prerequisites. Learning Outcomes
Cartesian Components of Vectors 9.2 Introduction It is useful to be able to describe vectors with reference to specific coordinate sstems, such as the Cartesian coordinate sstem. So, in this Section, we
More informationChapter 11 Quadratic Functions
Chapter 11 Quadratic Functions Mathematical Overview The relationship among parabolas, quadratic functions, and quadratic equations is investigated through activities that eplore both the geometric and
More informationFunctions. Essential Question What is a function?
3. Functions COMMON CORE Learning Standard HSF-IF.A. Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs
More information3.2 Introduction to Functions
8 CHAPTER Graphs and Functions Write each statement as an equation in two variables. Then graph each equation. 97. The -value is more than three times the -value. 98. The -value is - decreased b twice
More informationAre You Ready? Find Area in the Coordinate Plane
SKILL 38 Are You Read? Find Area in the Coordinate Plane Teaching Skill 38 Objective Find the areas of figures in the coordinate plane. Review with students the definition of area. Ask: Is the definition
More informationFunctions. Essential Question What is a function? Work with a partner. Functions can be described in many ways.
. Functions Essential Question What is a function? A relation pairs inputs with outputs. When a relation is given as ordered pairs, the -coordinates are inputs and the -coordinates are outputs. A relation
More informationSolving Systems Using Tables and Graphs
3-1 Solving Sstems Using Tables and Graphs Vocabular Review 1. Cross out the equation that is NOT in slope-intercept form. 1 5 7 r 5 s a 5!3b 1 5 3 1 7 5 13 Vocabular Builder linear sstem (noun) LIN ee
More informationACTIVITY: Using a Table to Plot Points
.5 Graphing Linear Equations in Standard Form equation a + b = c? How can ou describe the graph of the ACTIVITY: Using a Table to Plot Points Work with a partner. You sold a total of $6 worth of tickets
More informationShenandoah University. (PowerPoint) LESSON PLAN *
Shenandoah University (PowerPoint) LESSON PLAN * NAME DATE 10/28/04 TIME REQUIRED 90 minutes SUBJECT Algebra I GRADE 6-9 OBJECTIVES AND PURPOSE (for each objective, show connection to SOL for your subject
More information6.4 graphs OF logarithmic FUnCTIOnS
SECTION 6. graphs of logarithmic functions 9 9 learning ObjeCTIveS In this section, ou will: Identif the domain of a logarithmic function. Graph logarithmic functions. 6. graphs OF logarithmic FUnCTIOnS
More informationANALYTICAL GEOMETRY Revision of Grade 10 Analytical Geometry
ANALYTICAL GEOMETRY Revision of Grade 10 Analtical Geometr Let s quickl have a look at the analtical geometr ou learnt in Grade 10. 8 LESSON Midpoint formula (_ + 1 ;_ + 1 The midpoint formula is used
More informationFor use after the chapter Graphing Linear Equations and Functions 3 D. 7. 4y 2 3x 5 4; (0, 1) x-intercept: 6 y-intercept: 3.
Chapter Test A Write the coordinates of the point.. A. B. D. C. A. D C B.... Tell whether the ordered pair is a solution of the equation.. ; (, ) 7.. ; (, ). 7. ; (, ). Draw the line that has the given
More informationThe slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope.
LESSON Relating Slope and -intercept to Linear Equations UNDERSTAND The slope of a line is the ratio of the line s vertical change, called the rise, to its horizontal change, called the run. You can find
More information13.2 Exponential Growth Functions
Name Class Date. Eponential Growth Functions Essential Question: How is the graph of g () = a b - h + k where b > related to the graph of f () = b? A.5.A Determine the effects on the ke attributes on the
More informationChapter 9 BUILD YOUR VOCABULARY
C H A P T E R 9 BUILD YUR VCABULARY Chapter 9 This is an alphabetical list of new vocabular terms ou will learn in Chapter 9. As ou complete the stud notes for the chapter, ou will see Build Your Vocabular
More informationPRINCIPLES OF MATHEMATICS 11 Chapter 2 Quadratic Functions Lesson 1 Graphs of Quadratic Functions (2.1) where a, b, and c are constants and a 0
PRINCIPLES OF MATHEMATICS 11 Chapter Quadratic Functions Lesson 1 Graphs of Quadratic Functions (.1) Date A. QUADRATIC FUNCTIONS A quadratic function is an equation that can be written in the following
More informationCircles in the Coordinate Plane. Find the length of each segment to the nearest tenth y. Distance Formula Square both sides.
-5 ircles in the oordinate Plane -5. Plan What You ll Learn To write an equation of a circle To find the center and radius of a circle... nd Wh To describe the position and range of three cellular telephone
More informationEssential Question How can you solve a system of linear equations? $15 per night. Cost, C (in dollars) $75 per Number of. Revenue, R (in dollars)
5.1 Solving Sstems of Linear Equations b Graphing Essential Question How can ou solve a sstem of linear equations? Writing a Sstem of Linear Equations Work with a partner. Your famil opens a bed-and-breakfast.
More information2. Domain: The set of all abscissas (x s) of the ordered pairs (abscissa is the first element of an ordered pair)
. Relations and Functions. Relation: A set of ordered pairs E:,4,,5,,, 8,4. The set of all abscissas s of the ordered pairs abscissa is the first element of an ordered pair. Range: The set of all ordinates
More informationDiscrete and Continuous Domains
. Discrete and Continuous Domains How can ou decide whether the domain of a function is discrete or continuous? EXAMPLE: Discrete and Continuous Domains In Activities and in Section., ou studied two real-life
More information1Write and graph. 2Solve problems. Now. Then. Why? New Vocabulary
Direct Variation Then You found rates of change of linear functions. (Lesson -) Now Write and graph direct variation equations. Solve problems involving direct variation. Wh? Bianca is saving her mone
More information1.2 Inductive Reasoning
1.2 Inductive Reasoning Goal Use inductive reasoning to make conjectures. Key Words conjecture inductive reasoning counterexample Scientists and mathematicians look for patterns and try to draw conclusions
More informationNAME DATE PERIOD. Study Guide and Intervention. Ax + By = C, where A 0, A and B are not both zero, and A, B, and C are integers with GCF of 1.
NAME DATE PERID 3-1 Stud Guide and Intervention Graphing Linear Equations Identif Linear Equations and Intercepts A linear equation is an equation that can be written in the form A + B = C. This is called
More informationChapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs
Ch 5 Alg Note Sheet Ke Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Definition: Standard Form of a Quadratic Function The
More informationRepresent Relations and Functions
TEKS. a., a., a.5, A..A Represent Relations and Functions Before You solved linear equations. Now You will represent relations and graph linear functions. Wh? So ou can model changes in elevation, as in
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 informationSystems of Linear Equations: Solving by Graphing
8.1 Sstems of Linear Equations: Solving b Graphing 8.1 OBJECTIVE 1. Find the solution(s) for a set of linear equations b graphing NOTE There is no other ordered pair that satisfies both equations. From
More informationMATH 152 COLLEGE ALGEBRA AND TRIGONOMETRY UNIT 1 HOMEWORK ASSIGNMENTS
0//0 MATH COLLEGE ALGEBRA AND TRIGONOMETRY UNIT HOMEWORK ASSIGNMENTS General Instructions Be sure to write out all our work, because method is as important as getting the correct answer. The answers to
More informationLaurie s Notes. Overview of Section 3.5
Overview of Section.5 Introduction Sstems of linear equations were solved in Algebra using substitution, elimination, and graphing. These same techniques are applied to nonlinear sstems in this lesson.
More informationYou studied exponential growth and decay functions.
TEKS 7. 2A.4.B, 2A..B, 2A..C, 2A..F Before Use Functions Involving e You studied eponential growth and deca functions. Now You will stud functions involving the natural base e. Wh? So ou can model visibilit
More information5 Linear Graphs and Equations
Linear Graphs and Equations. Coordinates Firstl, we recap the concept of (, ) coordinates, illustrated in the following eamples. Eample On a set of coordinate aes, plot the points A (, ), B (0, ), C (,
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 informationDerivatives 2: The Derivative at a Point
Derivatives 2: The Derivative at a Point 69 Derivatives 2: The Derivative at a Point Model 1: Review of Velocit In the previous activit we eplored position functions (distance versus time) and learned
More informationMaths A Level Summer Assignment & Transition Work
Maths A Level Summer Assignment & Transition Work The summer assignment element should take no longer than hours to complete. Your summer assignment for each course must be submitted in the relevant first
More information74 Maths Quest 10 for Victoria
Linear graphs Maria is working in the kitchen making some high energ biscuits using peanuts and chocolate chips. She wants to make less than g of biscuits but wants the biscuits to contain at least 8 g
More information10.7. Interpret the Discriminant. For Your Notebook. x5 2b 6 Ï} b 2 2 4ac E XAMPLE 1. Use the discriminant KEY CONCEPT
10.7 Interpret the Discriminant Before You used the quadratic formula. Now You will use the value of the discriminant. Wh? So ou can solve a problem about gmnastics, as in E. 49. Ke Vocabular discriminant
More informationGlossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards
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 informationMaintaining Mathematical Proficiency
Name Date Chapter 8 Maintaining Mathematical Proficienc Graph the linear equation. 1. = 5. = + 3 3. 1 = + 3. = + Evaluate the epression when =. 5. + 8. + 3 7. 3 8. 5 + 8 9. 8 10. 5 + 3 11. + + 1. 3 + +
More informationP.4 Lines in the Plane
28 CHAPTER P Prerequisites P.4 Lines in the Plane What ou ll learn about Slope of a Line Point-Slope Form Equation of a Line Slope-Intercept Form Equation of a Line Graphing Linear Equations in Two Variables
More informationGraph and Write Equations of Ellipses. You graphed and wrote equations of parabolas and circles. You will graph and write equations of ellipses.
TEKS 9.4 a.5, A.5.B, A.5.C Before Now Graph and Write Equations of Ellipses You graphed and wrote equations of parabolas and circles. You will graph and write equations of ellipses. Wh? So ou can model
More informationPre-AP Algebra 2 Lesson 1-5 Linear Functions
Lesson 1-5 Linear Functions Objectives: Students will be able to graph linear functions, recognize different forms of linear functions, and translate linear functions. Students will be able to recognize
More informationSTUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE. Functions & Graphs
STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE Functions & Graphs Contents Functions and Relations... 1 Interval Notation... 3 Graphs: Linear Functions... 5 Lines and Gradients... 7 Graphs: Quadratic
More informationChapter 13 Resource Masters
Chapter 13 Resource Masters Consumable Workbooks Man of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Stud Guide
More informationEXAMPLE EXAMPLE. Simplify. Simplify each expression. See left. EXAMPLE Real-World Problem Solving EXAMPLE. Write = xa1 1!5 B = 162 Cross multiply.
-. Plan Lesson Preview Check Skills You ll Need Operations With Radical Epressions Lesson -: Eamples,, 7 Eercises, Etra Practice, p. 7 Lesson Preview What You ll Learn - To simplify sums and differences
More informationAnalytic Geometry 300 UNIT 9 ANALYTIC GEOMETRY. An air traffi c controller uses algebra and geometry to help airplanes get from one point to another.
UNIT 9 Analtic Geometr An air traffi c controller uses algebra and geometr to help airplanes get from one point to another. 00 UNIT 9 ANALYTIC GEOMETRY Copright 00, K Inc. All rights reserved. This material
More informationSYSTEMS OF THREE EQUATIONS
SYSTEMS OF THREE EQUATIONS 11.2.1 11.2.4 This section begins with students using technology to eplore graphing in three dimensions. By using strategies that they used for graphing in two dimensions, students
More informationChapter 4 Resource Masters
Chapter Resource Masters Reading to Learn Mathematics Vocabular Builder This is an alphabetical list of the ke vocabular terms ou will learn in Chapter. As ou stud the chapter, complete each term s definition
More informationUNIT 6 MODELING GEOMETRY Lesson 1: Deriving Equations Instruction
Prerequisite Skills This lesson requires the use of the following skills: appling the Pthagorean Theorem representing horizontal and vertical distances in a coordinate plane simplifing square roots writing
More informationLesson 9.1 Using the Distance Formula
Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)
More informationWarm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
2-4 Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Write a conditional statement from each of the following. 1. The intersection of two lines is a point. If two lines intersect, then they intersect
More information10.2 Graphing Exponential Functions
Name Class Date 10. Graphing Eponential Functions Essential Question: How do ou graph an eponential function of the form f () = ab? Resource Locker Eplore Eploring Graphs of Eponential Functions Eponential
More informationVocabulary. Term Page Definition Clarifying Example degree of a monomial. degree of a polynomial. end behavior. leading coefficient.
CHAPTER 6 Vocabular The table contains important vocabular terms from Chapter 6. As ou work through the chapter, fill in the page number, definition, and a clarifing eample. Term Page Definition Clarifing
More informationWriting Equations in Point-Slope Form
. Writing Equations in Point-Slope Form Essential Question How can ou write an equation of a line when ou are given the slope and a point on the line? Writing Equations of Lines Work with a partner. Sketch
More informationIDAHO EXTENDED CONTENT STANDARDS MATHEMATICS
Standard 1: Number and Operation Goal 1.1: Understand and use numbers. K.M.1.1.1A 1.M.1.1.1A Recognize symbolic Indicate recognition of expressions as numbers various # s in environments K.M.1.1.2A Demonstrate
More informationCHAPTER 7. Think & Discuss (p. 399) x is curved and not a. x 0. straight line r r 3. 6 cm r. Skill Review (p.
CHAPTER Think & Discuss (p. 99). (, 8) because the graph is curved and not a straight line. about kg; locate mm on the graph and read the curve at the point directl above mm. Skill Review (p. ).......
More informationGraph and Write Equations of Parabolas
TEKS 9.2 a.5, 2A.5.B, 2A.5.C Graph and Write Equations of Parabolas Before You graphed and wrote equations of parabolas that open up or down. Now You will graph and write equations of parabolas that open
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 informationComparing Linear, Exponential, and Quadratic Functions
. Comparing Linear, Eponential, and Quadratic Functions How can ou compare the growth rates of linear, eponential, and quadratic functions? ACTIVITY: Comparing Speeds Work with a partner. Three cars start
More information3.2 Understanding Relations and Functions-NOTES
Name Class Date. Understanding Relations and Functions-NOTES Essential Question: How do ou represent relations and functions? Eplore A1.1.A decide whether relations represented verball, tabularl, graphicall,
More informationUnderstanding Part 2 of The Fundamental Theorem of Calculus
Understanding Part of The Fundamental Theorem of Calculus Worksheet 8: The Graph of F () What is an Anti-Derivative? Give an eample that is algebraic: and an eample that is graphical: eample : Below is
More informationWelcome to IB Math - Standard Level Year 2
Welcome to IB Math - Standard Level Year 2 Why math? Not So Some things to know: Good HW Good HW Good HW www.aleimath.blogspot.com Example 1. Lots of info at Example Example 2. HW yup. You know you love
More informationMATH 60 Course Notebook Chapter #1
MATH 60 Course Notebook Chapter #1 Integers and Real Numbers Before we start the journey into Algebra, we need to understand more about the numbers and number concepts, which form the foundation of Algebra.
More information4.2 Parabolas. Explore Deriving the Standard-Form Equation. Houghton Mifflin Harcourt Publishing Company. (x - p) 2 + y 2 = (x + p) 2
COMMON CORE. d Locker d LESSON Parabolas Common Core Math Standards The student is epected to: COMMON CORE A-CED.A. Create equations in two or more variables to represent relationships between quantities;
More information9.3. Practice C For use with pages Tell whether the triangle is a right triangle.
LESSON 9.3 NAME DATE For use with pages 543 549 Tell whether the triangle is a right triangle. 1. 21 2. 3. 75 6 2 2 17 72 63 66 16 2 4. 110 5. 4.3 6. 96 2 4.4 10 3 3 4.5 Decide whether the numbers can
More informationLesson 4.1 Interpreting Graphs
Lesson 4.1 Interpreting Graphs 1. Describe the pattern of the graph of each of the following situations as the graphs are read from left to right as increasing, decreasing, increasing and then decreasing,
More information7.1 Connecting Intercepts and Zeros
Locker LESSON 7. Connecting Intercepts and Zeros Common Core Math Standards The student is epected to: F-IF.7a Graph linear and quadratic functions and show intercepts, maima, and minima. Also A-REI.,
More information10-1 L E S S O N M A S T E R. Name. Vocabulary. 1. Refer to the diagram at the right. Fill in the blank. a. The leg adjacent to is.
L E S S O N M S T E R Vocabular 10 Questions on SPUR Objectives 1. Refer to the diagram at the right. Fill in the blank. a. The leg adjacent to is. b. The leg opposite is. c. The hpotenuse is. C 2. Fill
More informationDomain, Range, and End Behavior
Locker LESSON 1.1 Domain, Range, and End Behavior Common Core Math Standards The student is epected to: F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship
More information