Regents Exam Questions
A.REI.C.7: Quadratic-Linear Systems 4
Name: ________________________
www.jmap.org
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 = x 2 + 4x − 5
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 = x 2 + 4x − 5
y = x−1
y = 2x + 3
1
Regents Exam Questions
A.REI.C.7: Quadratic-Linear Systems 4
Name: ________________________
www.jmap.org
3 Solve the following system of equations
algebraically or graphically for x and y:
y = x 2 + 2x − 1
5 Solve the following system of equations
algebraically or graphically for x and y:
y = x 2 − 4x + 3
y = 3x + 5
y = x−1
6 Solve the following system of equations
algebraically or graphically for x and y:
y = x 2 + 4x + 6
4 Solve the following system of equations:
y = x 2 + 4x + 1
y = 5x + 3
[The use of the grid is optional.]
y = 2x + 6
2
Regents Exam Questions
A.REI.C.7: Quadratic-Linear Systems 4
Name: ________________________
www.jmap.org
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 = x 2 − 6x + 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 = x 2 − 4x − 5
2x + y = 5
y + 3x = 1
3
Regents Exam Questions
A.REI.C.7: Quadratic-Linear Systems 4
Name: ________________________
www.jmap.org
9 On the set of axes below, solve the following
system of equations graphically for all values of x
and y.
y = x 2 − 6x + 1
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 = 6
y = −2x + 4
4
Regents Exam Questions
A.REI.C.7: Quadratic-Linear Systems 4
Name: ________________________
www.jmap.org
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 = −x 2 + 6x − 3
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
x+y = 7
y + 1 = −2x
5
Regents Exam Questions
A.REI.C.7: Quadratic-Linear Systems 4
Name: ________________________
www.jmap.org
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 = x 2 + 4x + 2
14 Solve the following system of equations
graphically. State the coordinates of all points in
the solution.
y + 4x = x 2 + 5
y − 2x = 5
x+y = 5
6
Regents Exam Questions
A.REI.C.7: Quadratic-Linear Systems 4
Name: ________________________
www.jmap.org
15 On the set of axes below, graph the following
system of equations.
y + 2x = x 2 + 4
16 Solve the following system of equations
graphically.
2x 2 − 4x = y + 1
y−x = 4
Using the graph, determine and state the
coordinates of all points in the solution set for the
system of equations.
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
7
Regents Exam Questions
A.REI.C.7: Quadratic-Linear Systems 4
Name: ________________________
www.jmap.org
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
19 A rocket is launched from the ground and follows a
parabolic path represented by the equation
y = −x 2 + 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.
2y + 16 = 4x
8
ID: A
A.REI.C.7 Quadratic-Linear Systems 4
Answer Section
1 ANS:
.
REF: 080839ia
2 ANS:
REF: 011437ia
3 ANS:
. y = 3x + 5
(3,14) and (−2,−1).
.
= 3(3) + 5 = 14
= 3(−2) + 5 = −1
REF: 069935a
1
.
ID: A
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
2
.
ID: A
6 ANS:
. y = 2x + 6
.
.
= 2(0) + 6 = 6
= 2(−2) + 6 = 2
REF: 080839a
7 ANS:
REF: fall0738ia
3
ID: A
8 ANS:
.
REF: 061637ia
9 ANS:
REF: 060939ia
10 ANS:
REF: 061039ia
4
ID: A
11 ANS:
REF: 081138ia
12 ANS:
REF: 081337ia
13 ANS:
REF: 011636ge
5
ID: A
14 ANS:
REF: 061535ge
15 ANS:
REF: 011339ia
16 ANS:
REF: 061137ge
6
ID: A
17 ANS:
REF: 011038ge
18 ANS:
REF: 061238ge
7
ID: A
19 ANS:
. y = −x + 10
.
.
= −(10) + 10 = 0
= −(1) + 10 = 9
REF: 060235a
8
.