Graphing Quadratic Functions Group Testreview

Graphing Quadratic Functions Group TestREVIEW

Directions: 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 +4

2.Graph the quadratic function. Label the vertex and axis of symmetry.

y = x2 – 3x + 4

3.Graph y = -(x – 3)2 + 1

4.Graph the parabola:y = (x + 4)2 -2

5.Sketch the graph of the equation. y = x2 – 3x + 2

6.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 - 2

Writing: Choose 2 problems from this section.

8.Find the vertex and the axis of symmetry of the parabola. y = x2 +2x + 1

x = -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 up

10.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 units

Min or Max:Find the maximum value or minimum value for the function. Choose One.

12.y = -4x2 + 8x + 2

Max 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 equationy = ax2 -12x + c hasa 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 units

16.How would you translate the graph of to produce the graph of y = x2 +5 ?

You would move it down the y-axis 5 units

In 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 - 3

Move it 4 units left and 3 units down

18.

Move it 4 units right and 1 unit up

Writing: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 + 2from 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 24OR you can just do 25from 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. onex-intercept b. two x-intercepts

c. threex-intercepts d. no x-intercepts

e. oney-intercept f. two y-intercepts

Answers 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 + 1

27.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 + 6

Finding 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 Test

Answer Section

1.ANS:

PTS:1DIF:Level BREF:MAL20515NAT:NT.CCSS.MTH.10.9-12.F-IF.7.a

STA: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.A TOP: Lesson 4.1 Graph Quadratic Functions in Standard Form

KEY:graph | quadraticMSC:KnowledgeNOT:978-0-547-31541-6

2.ANS:

Move the graph of up 10units to get the graph of .

PTS:1DIF:Level BREF:MAL20520STA:TX.TEKS.MTH.05.AL2.6.B

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.e

TOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:translation | parabola

MSC:AnalysisNOT:978-0-547-31541-6

3.ANS:

axis of symmetry: x =

vertex: (, )

PTS:1DIF:Level BREF:MAL20521NAT:NT.CCSS.MTH.10.9-12.F-IF.7.a

STA: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.A

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.1 Graph Quadratic Functions in Standard Form

KEY:graph | parabola | vertex | axis of symmetry | quadraticMSC:Knowledge

NOT:978-0-547-31541-6

4.ANS:

Vertex: (2, 4); Axis: x = 2

PTS:1DIF:Level BREF:MAL20523STA:TX.TEKS.MTH.05.AL2.5.C

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:parabola | vertex | axis of symmetry

MSC:KnowledgeNOT:978-0-547-31541-6

5.ANS:

Vertex: (-2, 15); Opens down

PTS:1DIF:Level BREF:MAL20524STA:TX.TEKS.MTH.05.AL2.5.C

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:parabola | vertex | down | up

MSC:KnowledgeNOT:978-0-547-31541-6

6.ANS:

PTS:1DIF:Level BREF:MAL20526NAT:NT.CCSS.MTH.10.9-12.F-IF.7.a

STA: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.A TOP: Lesson 4.1 Graph Quadratic Functions in Standard Form

KEY:graph | parabolaMSC:KnowledgeNOT:978-0-547-31541-6

7.ANS:

PTS:1DIF:Level BREF:MAL20527NAT:NT.CCSS.MTH.10.9-12.F-IF.7.a

STA: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.A TOP: Lesson 4.1 Graph Quadratic Functions in Standard Form

KEY:graph | parabolaMSC:KnowledgeNOT:978-0-547-31541-6

8.ANS:

vertex: ; axis of symmetry:

PTS:1DIF:Level BREF:MAL20529NAT:NT.CCSS.MTH.10.9-12.F-IF.7.a

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c | NCTM.PSSM.00.MTH.9-12.ALG.1.e

TOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:graph | parabola | quadratic

MSC:KnowledgeNOT:978-0-547-31541-6

9.ANS:

Sample answer:A quadratic function is a function of the form where The function is a quadratic function.

PTS:1DIF:Level BREF:MAL20535

STA: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.A

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c | NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-12.COM.4 | NCTM.PSSM.00.MTH.9-12.REP.1 | NCTM.PSSM.00.MTH.9-12.REP.3 TOP: Lesson 4.1 Graph Quadratic Functions in Standard Form

KEY:write | quadratic | functionMSC:Comprehension

NOT:978-0-547-31541-6

10.ANS:

maximum: 13

PTS:1DIF:Level BREF:MAL21426NAT:NT.CCSS.MTH.10.9-12.A-SSE.3.b

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:quadratic | function | maximum

MSC:ComprehensionNOT:978-0-547-31541-6

11.ANS:

minimum: 0.75

PTS:1DIF:Level BREF:MAL21427NAT:NT.CCSS.MTH.10.9-12.A-SSE.3.b

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:quadratic | function | minimum

MSC:ComprehensionNOT:978-0-547-31541-6

12.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 ygives . Solving for c yields c = 9. The equation is .

PTS:1DIF:Level AREF:A2.04.01.SR.02

TOP:Lesson 4.1 Graph Quadratic Functions in Standard FormKEY:Quadratic | vertex | short response

MSC:AnalysisNOT:978-0-547-31541-6

13.ANS:

PTS:1DIF:Level BREF:MAL20536NAT:NT.CCSS.MTH.10.9-12.F-IF.7.a

STA: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.A LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:graph | vertex formMSC:KnowledgeNOT:978-0-547-31541-6

14.ANS:

PTS:1DIF:Level BREF:MAL20538NAT:NT.CCSS.MTH.10.9-12.F-IF.7.a

STA: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.A LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:graph | vertex formMSC:KnowledgeNOT:978-0-547-31541-6

15.ANS:

PTS:1DIF:Level BREF:MAL20540

STA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.7.B

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:translation | parabolaMSC:Comprehension

NOT:978-0-547-31541-6

16.ANS:

PTS:1DIF:Level BREF:MAL20542

STA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.7.B

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:translation | parabolaMSC:Comprehension

NOT:978-0-547-31541-6

17.ANS:

3 units left and 4 units down

PTS:1DIF:Level BREF:MAL20543

STA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.7.B

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:translate | graphMSC:Comprehension

NOT:978-0-547-31541-6

18.ANS:

5 units right and 1 unit up

PTS:1DIF:Level BREF:MAL20544

STA:TX.TEKS.MTH.05.AL2.5.C | TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.7.B

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.c

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:translate | graphMSC:Comprehension

NOT:978-0-547-31541-6

19.ANS:

PTS:1DIF:Level BREF:MAL20552NAT:NT.CCSS.MTH.10.9-12.F-IF.7.a

STA: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.A

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:quadratic | relation | graph | parabolaMSC:Knowledge

NOT:978-0-547-31541-6

20.ANS:

Sample answers:

PTS:1DIF:Level BREF:MAL20555NAT:NT.CCSS.MTH.10.9-12.F-BF.3

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-12.GEO.3.a

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:square | variable | translate | equationMSC:Comprehension

NOT:978-0-547-31541-6

21.ANS:

Sample answers:

PTS:1DIF:Level BREF:MAL20556NAT:NT.CCSS.MTH.10.9-12.F-BF.3

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-12.GEO.3.a

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:equation | square | variable | translateMSC:Comprehension

NOT:978-0-547-31541-6

22.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:NT.CCSS.MTH.10.9-12.F-BF.3

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-12.GEO.3.a

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:graph | vertex form | translationMSC:Comprehension

NOT:978-0-547-31541-6

23.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:NT.CCSS.MTH.10.9-12.F-BF.3

LOC:NCTM.PSSM.00.MTH.9-12.ALG.1.e | NCTM.PSSM.00.MTH.9-12.GEO.3.a

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:graph | vertex form | translateMSC:Comprehension

NOT:978-0-547-31541-6

24.ANS:

Any equation of the form where a 0; sample: .

PTS:1DIF:Level BREF:MAL20561

STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.C

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:quadratic | function | maximum | axis of symmetryMSC:Comprehension

NOT:978-0-547-31541-6

25.ANS:

Any equation of the form where a 0; sample: .

PTS:1DIF:Level BREF:MAL20562

STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.C

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:quadratic | function | axis of symmetry |minimumMSC:Comprehension

NOT:978-0-547-31541-6

26.ANS:

Answers will vary. Examples are given.

a. b. c. not possible d. e. f.

PTS:1DIF:Level BREF:MAL20563

STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.C

TOP:Lesson 4.2 Graph Quadratic Functions in Vertex or Intercept Form

KEY:quadratic | equation | x-interceptsMSC:Comprehension

NOT:978-0-547-31541-6

27.ANS:

PTS:1DIF:Level BREF:MAL20718

STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.C

TOP:Lesson 4.10 Write Quadratic Functions and Models

KEY:equation | function | vertex form | parabola | vertexMSC:Knowledge

NOT:978-0-547-31541-6

28.ANS:

f(x)=x2

PTS:1DIF:Level AREF:MAL20719

STA:TX.TEKS.MTH.05.AL2.6.B | TX.TEKS.MTH.05.AL2.6.C

TOP:Lesson 4.10 Write Quadratic Functions and Models

KEY:parabola | vertex | equation | functionMSC:Knowledge

NOT:978-0-547-31541-6

29.ANS:

PTS:1DIF:Level BREF:A2.04.10.FR.29

TOP:Lesson 4.10 Write Quadratic Functions and Models

KEY:Free Response | write quadratic function | standard formMSC:Knowledge

NOT:978-0-547-31541-6

30.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 ayields . The final equation is .

PTS:1DIF:Level BREF:A2.04.10.SR.24

TOP:Lesson 4.10 Write Quadratic Functions and Models

KEY:Vertex | axis of symmetry | short responseMSC:Comprehension

NOT:978-0-547-31541-6