A.REI.C.7 Quadratic-Linear Systems 4 -...

Regents Exam Questions Name: ________________________ A.REI.C.7: Quadratic-Linear Systems 4www.jmap.org

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A.REI.C.7 Quadratic-Linear Systems 4

1 On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set.

y = x2 + 4x − 5

y = x − 1

2 On the set of axes below, solve the following system of equations graphically for all values of x and y. State the coordinates of all solutions.

y = x2 + 4x − 5

y = 2x + 3

Regents Exam Questions Name: ________________________ A.REI.C.7: Quadratic-Linear Systems 4www.jmap.org

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3 Solve the following system of equations algebraically or graphically for x and y:

y = x2 + 2x − 1

y = 3x + 5

4 Solve the following system of equations:y = x2 + 4x + 1

y = 5x + 3[The use of the grid is optional.]

5 Solve the following system of equations algebraically or graphically for x and y:

y = x2 − 4x + 3

y = x − 1

6 Solve the following system of equations algebraically or graphically for x and y:

y = x2 + 4x + 6

y = 2x + 6

Regents Exam Questions Name: ________________________ A.REI.C.7: Quadratic-Linear Systems 4www.jmap.org

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7 Solve the following systems of equations graphically, on the set of axes below, and state the coordinates of the point(s) in the solution set.

y = x2 − 6x + 5

2x + y = 5

8 On the set of axes below, solve the following system of equations graphically for all values of x and y. State the coordinates of all solutions.

y = x2 − 4x − 5

y + 3x = 1

Regents Exam Questions Name: ________________________ A.REI.C.7: Quadratic-Linear Systems 4www.jmap.org

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9 On the set of axes below, solve the following system of equations graphically for all values of x and y.

y = x2 − 6x + 1

y + 2x = 6

10 On the set of axes below, solve the following system of equations graphically for all values of x and y.

y = −x 2 − 4x + 12

y = −2x + 4

Regents Exam Questions Name: ________________________ A.REI.C.7: Quadratic-Linear Systems 4www.jmap.org

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11 On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution set.

y = −x2 + 6x − 3

x + y = 7

12 On the set of axes below, graph the following system of equations. Using the graph, determine and state all solutions of the system of equations.

y = −x 2 − 2x + 3

y + 1 = −2x

Regents Exam Questions Name: ________________________ A.REI.C.7: Quadratic-Linear Systems 4www.jmap.org

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13 On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution.

y = x2 + 4x + 2

y − 2x = 5

14 Solve the following system of equations graphically. State the coordinates of all points in the solution.

y + 4x = x2 + 5

x + y = 5

Regents Exam Questions Name: ________________________ A.REI.C.7: Quadratic-Linear Systems 4www.jmap.org

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15 On the set of axes below, graph the following system of equations.

y + 2x = x2 + 4

y − x = 4Using the graph, determine and state the coordinates of all points in the solution set for the system of equations.

16 Solve the following system of equations graphically.

2x2 − 4x = y + 1

x + y = 1

17 On the set of axes below, solve the following system of equations graphically for all values of x and y.

y = (x − 2)2 + 4

4x + 2y = 14

Regents Exam Questions Name: ________________________ A.REI.C.7: Quadratic-Linear Systems 4www.jmap.org

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18 On the set of axes below, solve the system of equations graphically and state the coordinates of all points in the solution.

y = (x − 2)2 − 3

2y + 16 = 4x

19 A rocket is launched from the ground and follows a parabolic path represented by the equation y = −x2 + 10x . At the same time, a flare is launched from a height of 10 feet and follows a straight path represented by the equation y = −x + 10. Using the accompanying set of axes, graph the equations that represent the paths of the rocket and the flare, and find the coordinates of the point or points where the paths intersect.

ID: A

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A.REI.C.7 Quadratic-Linear Systems 4Answer Section

1 ANS:

.

REF: 080839ia 2 ANS:

REF: 011437ia 3 ANS:

(3,14) and (−2,−1). . y = 3x + 5

= 3(3) + 5 = 14

= 3(−2) + 5 = −1

. .

REF: 069935a

ID: A

2

4 ANS:

. . y = 5x + 3

= 5(2) + 3 = 13

= 5(−1) + 3 = −2

. .

REF: 080538a 5 ANS:

. . y = x − 1

= (4) − 1 = 3

= (1) − 1 = 0

.

REF: 060839a

ID: A

3

6 ANS:

. . y = 2x + 6

= 2(0) + 6 = 6

= 2(−2) + 6 = 2

.

REF: 080839a 7 ANS:

REF: fall0738ia

ID: A

4

8 ANS:

.

REF: 061637ia 9 ANS:

REF: 060939ia 10 ANS:

REF: 061039ia

ID: A

5

11 ANS:

REF: 081138ia 12 ANS:

REF: 081337ia 13 ANS:

REF: 011636ge

ID: A

6

14 ANS:

REF: 061535ge 15 ANS:

REF: 011339ia 16 ANS:

REF: 061137ge

ID: A

7

17 ANS:

REF: 011038ge 18 ANS:

REF: 061238ge

ID: A

8

19 ANS:

. . y = −x + 10

= −(10) + 10 = 0

= −(1) + 10 = 9

. .

REF: 060235a