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Graphing Quadratic Functions Group Test REVIEWDirections: Each person will work at least 3 problems on this test. You will put your name by the problem you worked out. You group members will check your work and initial it.Graph: Choose 3 problems from this section.1.Graph y = x2 +42.Graph the quadratic function. Label the vertex and axis of symmetry. y = x2 – 3x + 43.Graph y = -(x – 3)2 + 1 4.Graph the parabola: y = (x + 4)2 -25.Sketch the graph of the equation. y = x2 – 3x + 26.Sketch the graph of the equation. y = x2 + 4x – 4 7.Graph the function. Label the vertex, axis of symmetry, and x-intercepts. y = - x2 + 4x - 2Writing: Choose 2 problems from this section.8.Find the vertex and the axis of symmetry of the parabola. y = x2 +2x + 1x = -b/2a x =-2/2(1) = -1 axis of symmetry y = (-1)2 +2(-1) + 1 =0 vertex is (-1,0)9.Find the vertex of the parabola and determine if it opens up or down. y = 3x2 – 6x + 4 x = -b/2a x =-(-6)/2(3) = 1 y = 3(1)2 -6(1) + 4=1 vertex(1,1) opens up10.Define quadratic function. Give an example of a quadratic function.A quadratic function is a function of the form where The function is a quadratic function.11.How would you translate the graph of to produce the graph of y = x2 - 8?You would move it down the y-axis 8 unitsMin or Max: Find the maximum value or minimum value for the function. Choose One.12. y = -4x2 + 8x + 2Max point at (1,6)13. f(x) = -x2 – 2x – 1 Max point at (-1, 0)Finding c: Choose One, either a or b.14.The graph of the equation y = ax2 -12x + c has a vertex of (-2, 13).a. Explain how to use the formula for the x-coordinate of the vertex to find the value of a.a. The value of the x-coordinate of the vertex is . In y = ax2 -12x + c , b = –12, so solve -2 = -12/2a for a: a = -3.b. Use the values of x and y from the vertex in the equation to find the value of c, then write the equation.b. We now have y = -3x2 – 12x +c . Substituting -2 for x and 13 for y gives 13 = -3(-2)2-12(-2) + c . Solving for c yields c = 1. The equation is y = -3x2 – 12x + 1 . Transformations: Choose 2 problems from this section. Either 15 and 17 or 16 and 18.15.How would you translate the graph of to produce the graph of y = (x + 7)2 You would move it left on the x-axis 7 units16.How would you translate the graph of to produce the graph of y = x2 +5 ?You would move it down the y-axis 5 unitsIn 17 & 18 Tell how to translate the graph of in order to produce the graph of the function.17. y = 0.2(x +4)2 - 3Move it 4 units left and 3 units down18. Move it 4 units right and 1 unit upWriting: Choose 2 problems from this section.19.Write three equations that show different ways in which the graph of the equation can be translated. At least one of the equations must describe a translation of the graph in two directions.Sample answers:20.Write three equations that show different ways in which the graph of can be translated. At least one of the equations must describe a translation of the graph in two directions.Sample answers:21.Writing: Explain how to obtain the graph of y = (x – 3)2 + 2 from the graph of .Then describe the graph of y = (x – 3)2 + 2.Sample answer: The graph of y = (x – 3)2 + 2 can be obtained by translating the graph of down 2 units and then 3 units to the right. The graph is a parabola with vertex (3, 2) that opens upward and is congruent to the graph of .22.Writing: Explain how to obtain the graph of y = (x+ 5)2 – 3 from the graph of .Then describe the graph of y = (x+ 5)2 – 3 .Sample answer:The graph of y = (x+ 5)2 – 3 can be obtained by translating the graph of down 3 units and then 5 units to the left. The graph is a parabola with vertex (-5, -3) that opens upward and is congruent to the graph of .Problem #: ____ Name ______________________Initials : ______ ______ ______ ______ Show answer and/or work below:Problem #: ____ Name ______________________Initials : ______ ______ ______ ______ Show answer and/or work below:Open-ended: Choose 23 and 24 OR you can just do 25 from this section.23.Open-ended: Find a quadratic function that has a maximum value of 4 and x = 2 as the line of symmetry for its graph. Any equation of the form y = -a(x -2)2 +4 where a ? 0; sample: y = -3(x -2)2 +4 .24.Open-ended: Find a quadratic function that has a minimum value of 2 and x = -1 as the line of symmetry for its graph.Any equation of the form y = a(x +1)2 +2 where a ? 0; sample: y = 2(x +1)2 +2 .25.Open-ended Problem: Write a quadratic equation, if possible, for a parabola that has the following intercepts. (Counts as 2 questions)a. one x-intercept b. two x-interceptsc. three x-intercepts d. no x-interceptse. one y-intercept f. two y-interceptsAnswers will vary. Examples are given.a. b. c. not possible d. e. f. Vertex & A Point: Choose both problems from this section.26.Write a quadratic function in vertex form that has the given vertex and passes through the given point.Vertex: (-4, 1); Point: (-2, 5) y = (x + 4)2 + 127.Write a quadratic function in vertex form that has the given vertex and passes through the given point.Vertex: (1,?6); Point: (-1,?2) y = -(x- 1)2 + 6Finding Equations: Every group must complete this question. It counts as 5 questions. 28.Find the equation for the parabola that has one x-intercept (6, 0), axis of symmetry x = 2, and maximum value 6. Explain how you got your answer:Answer: ______y = -3/8(x-2)2 + 6______________________Explanation: ___________Because the axis of symmetry is x =2 and the max is 6, the vertex is (2,6) Substitute this (x,y) value into the vertex form of a quadratic equation y = a(x – h )____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________. Graphing Quadratic Functions TestAnswer Section1.ANS:PTS:1DIF:Level BREF:MAL20515NAT:SS.MTH.10.9-12.F-IF.7.aSTA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.8.C | TX.TAKS.MTH.07.10.5.A.10.A | TX.TAKS.MTH.07.11.5.A.10.ATOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:graph | quadraticMSC:KnowledgeNOT:978-0-547-31541-62.ANS:Move the graph of up 10?units to get the graph of .PTS:1DIF:Level BREF:MAL20520STA:TX.TEKS.MTH.05.AL2.6.BLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.eTOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:translation | parabolaMSC:AnalysisNOT:978-0-547-31541-63.ANS:axis of symmetry: x = vertex: (, )PTS:1DIF:Level BREF:MAL20521NAT:SS.MTH.10.9-12.F-IF.7.aSTA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.8.C | TX.TAKS.MTH.07.10.5.A.10.A | TX.TAKS.MTH.07.11.5.A.10.ALOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:graph | parabola | vertex | axis of symmetry | quadraticMSC:KnowledgeNOT:978-0-547-31541-64.ANS:Vertex: (2, 4); Axis: x = 2PTS:1DIF:Level BREF:MAL20523STA:TX.TEKS.MTH.05.AL2.5.CLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:parabola | vertex | axis of symmetryMSC:KnowledgeNOT:978-0-547-31541-65.ANS:Vertex: (-2, 15); Opens downPTS:1DIF:Level BREF:MAL20524STA:TX.TEKS.MTH.05.AL2.5.CLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:parabola | vertex | down | upMSC:KnowledgeNOT:978-0-547-31541-66.ANS:PTS:1DIF:Level BREF:MAL20526NAT:SS.MTH.10.9-12.F-IF.7.aSTA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.8.C | TX.TAKS.MTH.07.10.5.A.10.A | TX.TAKS.MTH.07.11.5.A.10.ATOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:graph | parabolaMSC:KnowledgeNOT:978-0-547-31541-67.ANS:PTS:1DIF:Level BREF:MAL20527NAT:SS.MTH.10.9-12.F-IF.7.aSTA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.8.C | TX.TAKS.MTH.07.10.5.A.10.A | TX.TAKS.MTH.07.11.5.A.10.ATOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:graph | parabolaMSC:KnowledgeNOT:978-0-547-31541-68.ANS:vertex: ; axis of symmetry: PTS:1DIF:Level BREF:MAL20529NAT:SS.MTH.10.9-12.F-IF.7.aSTA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.8.C | TX.TAKS.MTH.07.9.5.A.9.C | TX.TAKS.MTH.07.10.5.A.9.C | TX.TAKS.MTH.07.10.5.A.10.A | TX.TAKS.MTH.07.11.5.A.9.C | TX.TAKS.MTH.07.11.5.A.10.ALOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c | NCTM.PSSM.00.MTH.9-12.ALG.1.eTOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:graph | parabola | quadraticMSC:KnowledgeNOT:978-0-547-31541-69.ANS:Sample answer:A quadratic function is a function of the form where The function is a quadratic function.PTS:1DIF:Level BREF:MAL20535STA:TX.TEKS.MTH.05.AL2.9.G | TX.TAKS.MTH.07.9.10.8.15.A | TX.TAKS.MTH.07.10.10.8.15.A | TX.TAKS.MTH.07.11.6.G.4.A | TX.TAKS.MTH.07.11.10.8.15.ALOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c | NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-.4 | NCTM.PSSM.00.MTH.9-12.REP.1 | NCTM.PSSM.00.MTH.9-12.REP.3TOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:write | quadratic | functionMSC:ComprehensionNOT:978-0-547-31541-610.ANS:maximum: 13PTS:1DIF:Level BREF:MAL21426NAT:SS.MTH.10.9-12.A-SSE.3.bLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:quadratic | function | maximumMSC:ComprehensionNOT:978-0-547-31541-611.ANS:minimum: 0.75PTS:1DIF:Level BREF:MAL21427NAT:SS.MTH.10.9-12.A-SSE.3.bLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:quadratic | function | minimumMSC:ComprehensionNOT:978-0-547-31541-612.ANS:a. The value of the x-coordinate of the vertex is . In , b = –4, so solve for a: a = 1.b. We now have . Substituting 2 for x and 5 for y gives . Solving for c yields c = 9. The equation is .PTS:1DIF:Level AREF:A2.04.01.SR.02TOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:Quadratic | vertex | short responseMSC:AnalysisNOT:978-0-547-31541-613.ANS:PTS:1DIF:Level BREF:MAL20536NAT:SS.MTH.10.9-12.F-IF.7.aSTA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.8.C | TX.TAKS.MTH.07.10.5.A.10.A | TX.TAKS.MTH.07.11.5.A.10.ALOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:graph | vertex formMSC:KnowledgeNOT:978-0-547-31541-614.ANS:PTS:1DIF:Level BREF:MAL20538NAT:SS.MTH.10.9-12.F-IF.7.aSTA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.8.C | TX.TAKS.MTH.07.10.5.A.10.A | TX.TAKS.MTH.07.11.5.A.10.ALOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:graph | vertex formMSC:KnowledgeNOT:978-0-547-31541-615.ANS:PTS:1DIF:Level BREF:MAL20540STA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.7.BLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:translation | parabolaMSC:ComprehensionNOT:978-0-547-31541-616.ANS:PTS:1DIF:Level BREF:MAL20542STA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.7.BLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:translation | parabolaMSC:ComprehensionNOT:978-0-547-31541-617.ANS:3 units left and 4 units downPTS:1DIF:Level BREF:MAL20543STA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.7.BLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:translate | graphMSC:ComprehensionNOT:978-0-547-31541-618.ANS:5 units right and 1 unit upPTS:1DIF:Level BREF:MAL20544STA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.7.BLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.cTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:translate | graphMSC:ComprehensionNOT:978-0-547-31541-619.ANS:PTS:1DIF:Level BREF:MAL20552NAT:SS.MTH.10.9-12.F-IF.7.aSTA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.8.C | TX.TAKS.MTH.07.10.5.A.10.A | TX.TAKS.MTH.07.11.5.A.10.ATOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:quadratic | relation | graph | parabolaMSC:KnowledgeNOT:978-0-547-31541-620.ANS:Sample answers:PTS:1DIF:Level BREF:MAL20555NAT:SS.MTH.10.9-12.F-BF.3STA:TX.TEKS.MTH.05.AL2.6.B | TX.TAKS.MTH.07.9.2.A.4.A | TX.TAKS.MTH.07.9.5.A.9.C | TX.TAKS.MTH.07.10.2.A.4.A | TX.TAKS.MTH.07.10.5.A.9.B | TX.TAKS.MTH.07.10.5.A.9.C | TX.TAKS.MTH.07.11.2.A.4.A | TX.TAKS.MTH.07.11.5.A.9.B | TX.TAKS.MTH.07.11.5.A.9.CLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-12.GEO.3.aTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:square | variable | translate | equationMSC:ComprehensionNOT:978-0-547-31541-621.ANS:Sample answers:PTS:1DIF:Level BREF:MAL20556NAT:SS.MTH.10.9-12.F-BF.3STA:TX.TEKS.MTH.05.AL2.6.B | TX.TAKS.MTH.07.9.2.A.4.A | TX.TAKS.MTH.07.9.5.A.9.C | TX.TAKS.MTH.07.10.2.A.4.A | TX.TAKS.MTH.07.10.5.A.9.B | TX.TAKS.MTH.07.10.5.A.9.C | TX.TAKS.MTH.07.11.2.A.4.A | TX.TAKS.MTH.07.11.5.A.9.B | TX.TAKS.MTH.07.11.5.A.9.CLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-12.GEO.3.aTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:equation | square | variable | translateMSC:ComprehensionNOT:978-0-547-31541-622.ANS:Sample answer:The graph of can be obtained by translating the graph of down 3 units and then 3 units to the left. The graph is a parabola with vertex (-3, -2) that opens upward and is congruent to the graph of .PTS:1DIF:Level BREF:MAL20559NAT:SS.MTH.10.9-12.F-BF.3STA:TX.TEKS.MTH.05.AL2.6.B | TX.TAKS.MTH.07.9.2.A.4.A | TX.TAKS.MTH.07.9.5.A.9.C | TX.TAKS.MTH.07.10.2.A.4.A | TX.TAKS.MTH.07.10.5.A.9.B | TX.TAKS.MTH.07.10.5.A.9.C | TX.TAKS.MTH.07.11.2.A.4.A | TX.TAKS.MTH.07.11.5.A.9.B | TX.TAKS.MTH.07.11.5.A.9.CLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-12.GEO.3.aTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:graph | vertex form | translationMSC:ComprehensionNOT:978-0-547-31541-623.ANS:Sample answer:The graph of can be obtained by translating the graph of down 3 units and then 5 units to the right. The graph is a parabola with vertex (5, -3) that opens upward and is congruent to the graph of .PTS:1DIF:Level BREF:MAL20560NAT:SS.MTH.10.9-12.F-BF.3STA:TX.TEKS.MTH.05.AL2.6.B | TX.TAKS.MTH.07.9.2.A.4.A | TX.TAKS.MTH.07.9.5.A.9.C | TX.TAKS.MTH.07.10.2.A.4.A | TX.TAKS.MTH.07.10.5.A.9.B | TX.TAKS.MTH.07.10.5.A.9.C | TX.TAKS.MTH.07.11.2.A.4.A | TX.TAKS.MTH.07.11.5.A.9.B | TX.TAKS.MTH.07.11.5.A.9.CLOC:NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-12.GEO.3.aTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:graph | vertex form | translateMSC:ComprehensionNOT:978-0-547-31541-624.ANS:Any equation of the form where a ? 0; sample: .PTS:1DIF:Level BREF:MAL20561STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.CTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:quadratic | function | maximum | axis of symmetryMSC:ComprehensionNOT:978-0-547-31541-625.ANS:Any equation of the form where a ? 0; sample: .PTS:1DIF:Level BREF:MAL20562STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.CTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:quadratic | function | axis of symmetry |minimumMSC:ComprehensionNOT:978-0-547-31541-626.ANS:Answers will vary. Examples are given.a. b. c. not possible d. e. f. PTS:1DIF:Level BREF:MAL20563STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.CTOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept FormKEY:quadratic | equation | x-interceptsMSC:ComprehensionNOT:978-0-547-31541-627.ANS:PTS:1DIF:Level BREF:MAL20718STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.CTOP:Lesson 4.10 Write Quadratic Functions and ModelsKEY:equation | function | vertex form | parabola | vertexMSC:KnowledgeNOT:978-0-547-31541-628.ANS:f(x)?=?x2PTS:1DIF:Level AREF:MAL20719STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.CTOP:Lesson 4.10 Write Quadratic Functions and ModelsKEY:parabola | vertex | equation | functionMSC:KnowledgeNOT:978-0-547-31541-629.ANS:PTS:1DIF:Level BREF:A2.04.10.FR.29TOP:Lesson 4.10 Write Quadratic Functions and ModelsKEY:Free Response | write quadratic function | standard formMSC:KnowledgeNOT:978-0-547-31541-630.ANS:The maximum value is 8, so the y-coordinate of the vertex is 8. The axis of symmetry is and since the axis of symmetry runs through the vertex, the x-coordinate of the vertex is 4. So the vertex is (4, 8). The vertex form of the equation is . Then substitute the values from (8, 0) into the equation to get . Solving for a yields . The final equation is .PTS:1DIF:Level BREF:A2.04.10.SR.24TOP:Lesson 4.10 Write Quadratic Functions and ModelsKEY:Vertex | axis of symmetry | short responseMSC:ComprehensionNOT:978-0-547-31541-6 ................
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