Answers (Anticipation Guide And Lesson 9-1)
Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 9DATEBefore you begin Chapter 9Quadratic and Exponential FunctionsAnticipation GuidePERIODA1AAfter you complete Chapter 9D9. A function containing powers is called an exponential function.Glencoe Algebra 1Answers3Glencoe Algebra 1 For those statements that you mark with a D, use a piece of paper to write anexample of why you disagree. Did any of your opinions about the statements change from the first column?Chapter 9DA10. Receiving compound interest on a bank account is one exampleof exponential growth.7. Any quadratic expression can be written as a perfect square bya method called completing the square.8. The quadratic formula can only be used to solve quadraticequations that cannot be solved by factoring or graphing.DA6. All quadratic equations have two real solutions.A5. The x-intercepts of the graph of a quadratic function are thesolutions to the related quadratic equation.DDASTEP 2AoD4. The graph of a quadratic function opening upward has nomaximum value.2. The graph of 4x2 – 2x 7 will be a parabola opening downwardsince the coefficient of x2 is positive.3. A quadratic function’s axis of symmetry is either the x-axis orthe y-axis.1. The graph of a quadratic function is a parabola.Statement Reread each statement and complete the last column by entering an A or a D.Step 2STEP 1A, D, o NS Write A or D in the first column OR if you are not sure whether you agree ordisagree, write NS (Not Sure). Decide whether you Agree (A) or Disagree (D) with the statement. Read each statement.Step 19NAMECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Graphing Quadratic Functionsa function described by an equation of the form f(x) ax2 bx c,where a 0Example:y 2x2 3x 8PERIODOyxExample 2-70Oyxb. What is the domain and range of thisfunction?The domain (the x-values is all realnumbers. The range (the y-values) is allreal numbers less than or equal to 2,which is the maximum.Graph the ordered pairs in the table andconnect them with a smooth curve.-2-121-31-2-2-5-4y-7x-6a. Use a table of values to graphy -x2 - 6x - 7.yxChapter 9D: {x x is a realnumber.} R: {y y 2}O1. y x2 2x5D: {x x is a realnumber.} R: {y y -4}Oy2. y -x2 - 44xGlencoe Algebra 1D: {x x is a realnumber.}1R: {y y - }Oy3. y x2 - 3x 2Use a table of values to graph each function. Determine the domain and range.Exercisesb. What is the domain and range ofthis function?The domain (the x-values) is all realnumbers. The range (the y-values) is allreal numbers greater than or equal to-3, which is the minimum.Graph the ordered pairs in the table andconnect them with a smooth curve.1-24-33121-20y6x-1a. Use a table of values to graphy x2 - 4x 1.Example 1The parent graph of the family of quadratic fuctions is y x2. Graphs of quadratic functionshave a general shape called a parabola. A parabola opens upward and has a minimumpoint when the value of a is positive, and a parabola opens downward and has a maximumpoint when the value of a is negative.QuadraticFunctionDATEStudy Guide and InterventionCharacteristics of Quadratic Functions9-1NAMEAnswers (Anticipation Guide and Lesson 9-1)Lesson 9-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter Resources
A2Glencoe Algebra 1Graphing Quadratic FunctionsStudy Guide and InterventionDATE(-1, -1)x -1Oyxb. Find the coordinates of the vertex.Since the equation of the axis ofsymmetry is x -1 and the vertex lieson the axis, the x-coordinate of the vertexis -1.y 2x2 4x 1Original equationy 2(-1)2 4(-1) 1Substitute.y 2(1) - 4 1Simplify.y -1The vertex is at (-1, -1).yxChapter 9min; (0, 3);D: {x all reals},R: {y y 3}; x 0O1. y x2 3x6max; (-2, 0);D: {x all reals},R: {y y 0}; x -2Oy2. y -x2 - 4x - 4xGlencoe Algebra 1min; (-1, 2);D: {x all reals},R: {y y 2}; x -1Oy3. y x2 2x 3Consider each equation. Determine whether the function has maximum orminimum value. State the maximum or minimum value. What are the domain andrange of the function? Find the equation of the axis of symmetry. Graph thefunction.Exercisesd. Graph the function.c. Identify the vertex as a maximum ora minimum.Since the coefficient of the x2-term ispositive, the parabola opens upward, andthe vertex is a minimum point.The axis of symmetry is x -1.2a4x - -12(2)bx - Example: The axis of symmetry ofy x2 2x 5 is the line x -1.Consider the graph of y 2x2 4x 1.2aFor the parabola y ax2 bx c, where a 0,bthe line x - is the axis of symmetry.a. Write the equation of the axis ofsymmetry.In y 2x2 4x 1, a 2 and b 4.Substitute these values into the equationof the axis of symmetry.ExampleAxis ofSymmetryParabolas have a geometric property called symmetry. Thatis, if the figure is folded in half, each half will match the other half exactly. The vertical linecontaining the fold line is called the axis of symmetry. The axis of symmetry contains theminimum or maximum point of the parabola, the vertex.(continued)PERIODCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 9Symmetry and Vertices9-1NAMEGraphing Quadratic FunctionsSkills PracticeDATEPERIODyxD all realsR {y y 3}Oy2. y -x2 3x(-2, 2); x -2; (0, 6)5. y x2 4x 6(-2, 15); x -2; (0, 3)6. y -3x2 - 12x 3Chapter 9Of(x)x10. f(x) -x2 - 2x 2Graph each function.minimum; (0, 0);D all reals,R {y y 0 }7. y 2x2Of(x)7x11. f(x) 2x2 4x - 2minimum; (1, -6);D all reals,R {y y -6}8. y x2 - 2x - 5c. What are the domain and range of the function?b. State the maximum or minimum value.OxGlencoe Algebra 1f (x)12. f(x) -2x2 - 4x 6maximum; (2, 3);D all reals,R {y y 3}9. y -x2 4x - 1a. Determine whether the function has maximum or minimum value.Consider each equation.(2, -2); x 2; (0, 6)4. y 2x2 - 8x 6xD all realsR {y y – 7}Oy3. y x2 - 2x - 6Find the vertex, the equation of the axis of symmetry, and the y-intercept.D all realsR {y y – 4}O1. y x2 - 4Use a table of values to graph each function. State the domain the range.9-1NAMEAnswers (Lesson 9-1)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 9-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Chapter 9Graphing Quadratic FunctionsPracticeDATEPERIODxD: {x all reals}R: {y y -6}Oy2. y x2 - 6x 3xD: {x all reals}R: {y y 3}Oy(2, 3); x 2; (0, -5)5. y -2x2 8x - 5(0.5, 0); x 0.5; (0, 1)6. 4x2 - 4x 1A3xOf(x)x11. f(x) -2x2 8x - 3max; (2.5, -3.75);D: {x all reals},R: {y y -3.75}8. y -x2 5x - 10f (x)Ox12. f(x) 2x2 8x 132}R: {y y -11 D: {x all reals},12min; (-1 , -11 );3323 2x 4x - 99. y Chapter 9Glencoe Algebra 1Answers8Glencoe Algebra 1c. An outfielder catches the ball three feet above the ground. How far has the balltraveled horizontally when the outfielder catches it? 200 ftb. What is the maximum height reached by the baseball? 53 fta. What is the equation of the axis of symmetry? x 10013. BASEBALL A player hits a baseball into the outfield. The equation h -0.005x2 x 3gives the path of the ball, where h is the height and x is the horizontal distance the balltravels.Of(x)10. f(x) -x2 3Graph each function.min; (0.2, 1.8);D: {x all reals},R: {y y 1.8}7. y 5x2 - 2x 2Consider each equation. Determine whether the function has maximum orminimum value. State the maximum or minimum value. What are the domainand range of the function?(0, -9); x 0; (0, -9)4. y x2 - 9x3. y -2x2 - 8x - 5Find the vertex, the equation of the axis of symmetry, and the y-intercept.D: {x all reals}R: {y y 2}Oy1. y -x2 2Use a table of values to graph each function. Determine the domain and range.9-1NAMECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, 3.8487.9Height(y inches)Chapter 925 ft3. ARCHITECTURE A hotel’s mainentrance is in the shape of a parabolicarch. The equation y -x2 10x modelsthe arch height y for any distance x fromone side of the arch. Use a graph todetermine its maximum height.82. PHYSICS Mrs. Capwell’s physics classinvestigates what happens when a ball isgiven an initial push, rolls up, and thenback down an inclined plane. The classfinds that y -x2 6x accuratelypredicts the ball’s position y after rollingx seconds. On the graph of the equation,what would be the y value when x 4?Source: National Security 6)O-4-6-8-10-12-14-16-5 -4-3-2yxGlencoe Algebra 11c. Graph the equation and label itsvertex.b. What is the equation of the axis ofsymmetry? x -2or y x2 4x - 12a. Write the equation representing thearea of the deck. y (x - 2)(x 6)x 65. GEOMETRY Teddy is building therectangular deck shown below.(2, 64); After 2 seconds, the ballreaches its highest point, 64 ftabove the ground.4. SOFTBALL Olympic softball goldmedalist Michele Smith pitches acurveball with a speed of 64 feet persecond. If she throws the ball straightupward at this speed, the ball’s height h(in feet) after t seconds is given byh -16t2 64t. Find the coordinates ofthe vertex of the graph of the ball’sheight and interpret its meaning.Graphing Quadratic FunctionsWord Problem Practice1. OLYMPICS Olympics were held in1896 and have been held every four years(except 1916, 1940, and 1944).The winning height y in men’s polevault at any number Olympiad x canbe approximated by the equationy 0.37x2 4.3x 126. Complete thetable to estimate the pole vault heightsin each of the Olympic Games. Roundyour answers to the nearest tenth.9-1NAMEAnswers (Lesson 9-1)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 9-1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A4Glencoe Algebra 1Graphing Cubic FunctionsEnrichmentDATEPERIODParent Function: f(x) x30x–3–1–22–110–112(-2, 2)(0, -1)yChapter 9local maximum:(-1.3, -0.4);local minimum:(0, 1)10local maximum:(0, -1);local minimum:(-1, -2)xxGlencoe Algebra 1local maximum:(-1.8, -1.9);local minimum:(-0.2, -4.1)0x00xy3. y x3 3x2 x - 4y2. y -2x3 - 3x2 - 1y1. y 0.5x3 x2 - 1Use a table of values to graph each equation. Then use the graph to estimate thelocations of the local minimum and local maximum points.ExercisesGraph the ordered pairs, and connect them to create a smooth curve.The “S” shape extends to infinity in the positive y direction and tonegative infinity in the negative y direction.The local minimum is located at (0, –1). The local maximum islocated at (–2, 2).xyExampleUse a table of values to graph y x3 3x2 - 1. Then use the graphto estimate the locations of the local minimum and local maximum points.Domain: all real numbersRange: all real numbersf (x)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 9A cubic function is a polynomial written in the form of f(x) ax3 bx2 cx n,where a 0. Cubic functions do not have absolute minimum and maximum values likequadratic functions do, but they can have a local minimum and a local maximum point.9-1NAMEDATEPERIODSolving Quadratic Equations by GraphingStudy Guide and Interventionan equation of the form ax2 bx c 0, where a 0Solve x2 4x 3 0 bygraphing.Example 2Solve x2 - 6x 9 0 bygraphing.xChapter 9-3, -4Of(x)1. x2 7x 12 0x-44, -3-8-12-8-4O4x11f(x)48xxGlencoe Algebra 1no real rootsOf(x)3. x2 - 4x 5 0To solve x2 - 6x 9 0, you need to knowwhere the value of f(x) 0. The vertex of theparabola is the x-intercept. Thus, the onlysolution is 3.Of(x)2. x2 - x - 12 0Solve each equation by graphing.ExercisesTo solve x2 4x 3 0, you need to knowwhere the value of f(x) 0. This occurs atthe x-intercepts, -3 and -1.The solutions are -3 and -1.Of(x)Graph the related function f(x) x2 4x 3. Graph the related function f(x) x2 - 6x 9.The equation of the axis of symmetry isThe equation of the axis of symmetry is64or 3. The vertex is at (3, 0). Graphx x - or -2. The vertex is at (-2, -1).2(1)2(1)the vertex and several other points on eitherGraph the vertex and several other points onside of the axis of symmetry.either side of the axis of symmetry.Example 1The solutions of a quadratic equation are called the roots of the equation. The roots ofa quadratic equation can be found by graphing the related quadratic functionf(x) ax2 bx c and finding the x-intercepts or zeros of the function.Quadratic EquationSolve by Graphing9-2NAMEAnswers (Lesson 9-1 and Lesson 9-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 9-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Chapter 9DATE(continued)PERIODSolving Quadratic Equations by GraphingStudy Guide and Intervention-21-2-1Notice that the value of the function changesfrom negative to positive between the x-valuesof -5 and -4 and between -2 and -1.Of(x)A5Chapter 9-1 x 0,4 x 5Of(x)4. x2 - 4x - 1 0-6 x -5,-2 x -1Of(x)1. x 7x 9 02xxGlencoe Algebra 1Answers120 x 1,2 x 3Of(x)5. 4x2 - 12x 3 0-2 x -1,2 x 3Of(x)2. x - x - 4 02xxxxxGlencoe Algebra 1-2 x -1,3 x 4Of(x)6. x2 - 2x - 4 0no real rootsOf(x)3. x - 4x 6 02Solve each equation by graphing. If integral roots cannot be found, estimate theroots to the nearest tenth.ExercisesThe x-intercepts of the graph are between -5 and -4 and between -2 and -1.So one root is between -5 and -4, and the other root is between -2 and -1.-2-3-41-5-3f(x)xGraph the related function f(x) x2 6x 6.ExampleSolve x2 6x 6 0 by graphing. If integral roots cannot be found,estimate the roots by stating the consecutive integers between which the roots lie.The roots of a quadratic equation may not be integers. If exactroots cannot be found, they can be estimated by finding the consecutive integers betweenwhich the roots lie.Estimate Solutions9-2NAMECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.PERIODaxcOf(n)n4. n2 - 7n -10 2, 5Of (c)2. c2 6c 8 0 -4, -2-3.4, -0.6-5.5, -0.6Chapter 9O7. d2 6d -3Of(p)f (d )5. p2 4p 2 0dp130.3, 3.8Of (h)8. h2 1 4h-2.3, 1.3Of (x)6. x2 x - 3 0hxSolve each equation by graphing. If integral roots cannot be found,estimate the roots to the nearest tenth.Of(a)3. a2 - 2a -1 1O1. x2 - 2x 3 0 Øf(x)DATESolving Quadratic Equations by GraphingSkills PracticeSolve each equation by graphing.9-2NAMEGlencoe Algebra 1Answers (Lesson 9-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 9-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A6Glencoe Algebra 1xOf(w)w2. w2 6w 9 0 -3Of(b)3. b2 - 3b 4 0 Øb0.6, 4.4mChapter 930 ft14Oh (x)6v12xnGlencoe Algebra 1-12-6-12 -6 O612Of(n)-2.7, -1.3f (v)6. 2v2 8v -710. What is the length of the walkway between the two supports?9. Graph the function and determine its x-intercepts. -15, 15the height in feet of the support above the walkway,where x 0 represents the midpoint of the bridge.251 2support. The function h(x) - x 9 represents8. DESIGN A footbridge is suspended from a parabolicb. What are the two numbers? -2 and 4a. Graph the related function f(n) -n 2n 8 anddetermine its x-intercepts. -2, 427. NUMBER THEORY Two numbers have a sum of 2and a product of -8. The quadratic equation-n2 2n 8 0 can be used to determinethe two numbers.-4.6, 0.6OOpf(m)5. 2m2 5 10mf(p)4. p2 4p 3Solve each equation by graphing. If integral roots cannot be found, estimate theroots to the nearest tenth.O1. x2 - 5x 6 0 2, 3f (x)PERIODSolving Quadratic Equations by GraphingPracticeDATECopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 9Solve each equation by graphing.9-2NAMEy1 2 3 4 5(2,16)xChapter 9Photograph 6 in.7 in.xxFrame3. FRAMING A rectangular photograph is7 inches long and 6 inches wide. Thephotograph is framed using material xinches wide. If the area of the frame andphotograph combined is 156 squareinches, what is the width of the framingmaterial? 3 in.2. LIGHT Ayzha and Jeremy hold aflashlight so that the light falls on apiece of graph paper in the shape of aparabola. Ayzha and Jeremy sketch theshape of the parabola and find that theequation y x2 - 3x - 10 matches theshape of the light beam. Determine theroots of the function. -2 and 5O161412108642DATEPERIOD15O-2-3-4y1 2 3 4xBASee students’ work.Glencoe Algebra 1c. Translate the parabola so that thereare no roots. Label this curve B.See students’ work.b. On the coordinate plane above,translate the parabola so that there isonly one root. Label this curve A.-4-3-24321a. Approximate the solution bygraphing. -2 and 25. ENGINEERING The shape of a satellitedish is often parabolic because of thereflective qualities of parabolas. Supposea particular satellite dish is modeled bythe following equation.0.5x2 2 y(30 - w)w 81 gives w 3 or 27.A 3 in. by 27 in. sheet of paperwould work.4. WRAPPING PAPER Can a rectangularpiece of wrapping paper with an area of81 square inches have a perimeter of 60inches? (Hint: Let length 30 – w.)Explain. Solving the equationSolving Quadratic Equations by GraphingWord Problem Practice1. FARMING In order for Ray to decidehow much fertilizer to apply to his corncrop this year, he reviews records fromprevious years. He finds that his cropyield y depends on the amount offertilizer he applies to his fields xaccording to the equationy -x2 4x 12. Graph the function,and find the point at which Ray gets thehighest yield possible.9-2NAMEAnswers (Lesson 9-2)Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Lesson 9-2Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Chapter 9EnrichmentDATEPERIODMultiply by-3.A7( 15 )152Chapter 919 283y - x x-130305. (2, 2), (5, -3), (0, -1)1 21y - x - x 1443. (4, -4), (0, 1), (3, -2)21 21y - x - x 61. (1, 5), (0, 6), (2, 3)5Glencoe Algebra 1Answers16821 21y - x - x 46. (0, 4), (4, 0), (-4, 4)53 218y - x x4. (1, 3), (6, 0), (0, 0)25 2125y x x26262. (-5, 0), (0, 0), (8, 100)Find the equation of a parabola through each set of three points.1571 2y x x - 2.The equation of a parabola through the three points is7b 151 3b - 20 9 156-30a- 41 15second or third equation.-6 -75a - 15b -6 a 1To find b, substitute for a in either the0 25a 5b - 2First, substitute -2 for c in the second and third equations.Then solve those two equations as you would any system of two equations.Multiply the second equation by 5 and the third equation by -3.0 9a 3b - 2Multiply by 5.0 45a 15b - 10Use the general equation y ax2 bx c. By substituting the givenvalues for x and y, you get three equations.(0, -2): -2 c(3, 0):0 9a 3b c(5, 2):2 25a 5b cHere is how to approximate an equation of the parabola through thepoints (0, -2), (3, 0), and (5, 2).If you know two points on a straight line, you can find the equation ofthe line. To find the equation of a parabola, you need three points onthe curve.Parabolas Through Three Given Points9-2NAMEGlencoe Algebra 1Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.DATEPERIODf(x)0c 0x9Chapter 9Translation of8unit.f(x) x2 up 987. g(x) x2 Translation off(x) x2 up 20 units.4. h(x) 20 x2Translation off(x) x2 up 1 unit.1. g(x) x2 1xc 0f(x)0yh(x)xb. h(x) x2 - 3The function can be written as f(x) x2 c.The value of c is –3, and –3 0.Therefore, the graph of g(x) x2 – 3 is atranslation of the graph of f(x) x2 down3 units.17Translation off(x) x2 down 0.3 unit.8. h(x) x2 – 0.3Translation off(x) x2 down 2 units.5. g(x) –2 x2Translation off(x) x2 down 6 units.2. h(x) x2 – 622Glencoe Algebra 1Translation off(x) x2 down 4 units.9. g(x) x2 – 4Translation of1uni
Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Answers Chapter 9 A3 Glencoe Algebra 1 Copyright Glencoe/McGraw-Hill, a division of .
4 Step Phonics Quiz Scores Step 1 Step 2 Step 3 Step 4 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 . Zoo zoo Zoo zoo Yoyo yoyo Yoyo yoyo You you You you
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Participant's Workbook Financial Management for Managers Institute of Child Nutrition iii Table of Contents Introduction Intro—1 Lesson 1: Financial Management Lesson 1—1 Lesson 2: Production Records Lesson 2—1 Lesson 3: Forecasting Lesson 3—1 Lesson 4: Menu Item Costs Lesson 4—1 Lesson 5: Product Screening Lesson 5—1 Lesson 6: Inventory Control Lesson 6—1
Proportion for inverse variation! x 2 18! 12 x 1 4, y 1 12, y 2 18 48 18 x 2 Cross multiply. 8 ! 3 x 2 Simplify. 11-1 direct variation; y kx direct variation; of the form y inverse variation; of the form xy k Answers (Anticipation Guide and Lesson 11-1)
Lesson 41 Day 1 - Draft LESSON 42 - DESCRIPTIVE PARAGRAPH Lesson 42 Day 1 - Revise Lesson 42 Day 1 - Final Draft Lesson 42 - Extra Practice LESSON 43 - EXPOSITORY PARAGRAPH Lesson 43 Day 1 - Brainstorm Lesson 43 Day 1 - Organize Lesson 43 Day 1 - Draft LESSON 44 - EXPOSITORY PARAGRAPH Lesson 44 Day 1 - Revise
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Lesson 2 Earthquakes: Earth's Crust in Motion Introduction Anticipation Guide As an introduction to this lesson on Earthquakes give students an anticipation guide which they will return to at the end of the lessons on Earthquakes. Standards: 1.c, 1.d, 1.e, 1.f, 7.e Objectives Students will be able to Describe how stress forces affect rock.
the Anticipation Guide as a pretest for the lesson. Hold on to the pretest for debriefing during the assessment section of the lesson plan. Anticipation Guide Puberty Indicate True (T) or False (F) for each statement. _ 1. The changes during puberty are physical rather than emotional. _ 2. Puberty lasts 5 to 7 years in boys. _ 3.
