Name: ________________________ Class: ___________________ Date: __________
ID: A
Quadratic Exploration Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Tell whether the graph of the quadratic function y = −x 2 − 10x + 1 opens upward or downward. Explain.
a. Because a > 0, the parabola opens downward.
b. Because a < 0, the parabola opens downward.
c. Because a < 0, the parabola opens upward.
d. Because a > 0, the parabola opens upward.
____
2. Identify the vertex of the parabola. Then give the minimum or maximum value of the function.
a.
b.
c.
d.
____
The vertex is (3, 6), and the minimum is 6.
The vertex is (3, 6), and the maximum is 6.
The vertex is (3, 6), and the maximum is 3.
The vertex is (3, 6), and the minimum is 3.
3. Find the axis of symmetry of the graph of y = 3x 2 + 6x + 4 .
a. y = −1
b. x = −1
c. x = 1
d. y = 1
1
Name: ________________________
____
ID: A
4. A swim team member performs a dive from a 14-foot-high springboard. The parabola below shows the path
of her dive.
Which equation represents the axis of symmetry?
a. x = 3
c.
b. y = 3
d.
2
x = 23
y = 23
ID: A
Quadratic Exploration Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: B
Check that the function is in standard form.
y = −x 2 − 10x + 1
a = −1
Identify the value of a.
Since a < 0, the parabola opens downward.
Feedback
A
B
C
D
To determine the direction the parabola opens, find the value of a in the standard form
of the equation.
Correct!
If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.
If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.
PTS: 1
DIF: Average
REF: Page 592
OBJ: 9-1.3 Identifying the Direction of a Parabola
NAT: 12.5.1.e
STA: 8.G.21
TOP: 9-1 Identifying Quadratic Functions
2. ANS: B
The vertex is the highest or lowest point on the parabola. If a parabola opens upward, the vertex is the lowest
point. If a parabola opens downward, the vertex is the highest point. The maximum or minimum value is the
y-value of the vertex.
Feedback
A
B
C
D
The maximum or minimum value is the y-value of the vertex.
Correct!
The maximum or minimum value is the y-value of the vertex.
If a parabola opens upward, then there is a minimum value. If a parabola opens
downward, then there is a maximum value.
PTS: 1
DIF: Average
REF: Page 592
OBJ: 9-1.4 Identifying the Vertex and the Minimum or Maximum
NAT: 12.5.4.c
STA: A.G.10
TOP: 9-1 Identifying Quadratic Functions
1
ID: A
3. ANS: B
b
For a quadratic function y = ax 2 + bx + c , the axis of symmetry is the vertical line x = − 2a .
y = 3x 2 + 6x + 4
a = 3, b = 6
b
6
x = − 2a = − 2(3) = −1
Find the values of a and b.
Substitute the values into the formula.
Feedback
A
B
C
D
The axis of symmetry of a parabola is a vertical line. All the points it contains have the
same x-value, so the variable in the equation should be x and not y.
Correct!
Use the formula x = -b/2a to find the axis of symmetry.
Use the formula x = -b/2a to find the axis of symmetry.
PTS:
OBJ:
NAT:
4. ANS:
TOP:
1
DIF: Average
REF: Page 601
9-2.3 Finding the Axis of Symmetry by Using the Formula
12.5.1.e
STA: A.A.41
TOP: 9-2 Characteristics of Quadratic Functions
A
PTS: 2
REF: 080813ia
STA: A.G.10
Identifying the Vertex of a Quadratic Given Graph
2
Name: ________________________ Class: ___________________ Date: __________
ID: B
Quadratic Exploration Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. A swim team member performs a dive from a 14-foot-high springboard. The parabola below shows the path
of her dive.
Which equation represents the axis of symmetry?
a. y = 3
c.
b. x = 23
d.
x=3
y = 23
____
2. Find the axis of symmetry of the graph of y = −3x 2 + 6x − 4 .
a. y = −1
b. x = 1
c. x = −1
d. y = 1
____
3. Tell whether the graph of the quadratic function y = −3x 2 + 2x + 2 opens upward or downward. Explain.
a. Because a > 0, the parabola opens upward.
b. Because a > 0, the parabola opens downward.
c. Because a < 0, the parabola opens upward.
d. Because a < 0, the parabola opens downward.
1
Name: ________________________
____
ID: B
4. Identify the vertex of the parabola. Then give the minimum or maximum value of the function.
a.
b.
c.
d.
The vertex is (−1, − 6), and the maximum is –1.
The vertex is (−1, − 6), and the maximum is –6.
The vertex is (−1, − 6), and the minimum is –6.
The vertex is (−1, − 6), and the minimum is –1.
2
ID: B
Quadratic Exploration Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: C
PTS: 2
REF: 080813ia
STA: A.G.10
TOP: Identifying the Vertex of a Quadratic Given Graph
2. ANS: B
b
For a quadratic function y = ax 2 + bx + c , the axis of symmetry is the vertical line x = − 2a .
y = −3x 2 + 6x − 4
a = −3, b = 6
b
6
x = − 2a = − 2(−3) = 1
Find the values of a and b.
Substitute the values into the formula.
Feedback
A
B
C
D
Use the formula x = -b/2a to find the axis of symmetry.
Correct!
Use the formula x = -b/2a to find the axis of symmetry.
The axis of symmetry of a parabola is a vertical line. All the points it contains have the
same x-value, so the variable in the equation should be x and not y.
PTS: 1
DIF: Average
REF: Page 601
OBJ: 9-2.3 Finding the Axis of Symmetry by Using the Formula
NAT: 12.5.1.e
STA: A.A.41
TOP: 9-2 Characteristics of Quadratic Functions
3. ANS: D
Check that the function is in standard form.
y = −3x 2 + 2x + 2
a = −3
Identify the value of a.
Since a < 0, the parabola opens downward.
Feedback
A
B
C
D
If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.
To determine the direction the parabola opens, find the value of a in the standard form
of the equation.
If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.
Correct!
PTS: 1
DIF: Average
REF: Page 592
OBJ: 9-1.3 Identifying the Direction of a Parabola
NAT: 12.5.1.e
STA: 8.G.21
TOP: 9-1 Identifying Quadratic Functions
1
ID: B
4. ANS: C
The vertex is the highest or lowest point on the parabola. If a parabola opens upward, the vertex is the lowest
point. If a parabola opens downward, the vertex is the highest point. The maximum or minimum value is the
y-value of the vertex.
Feedback
A
B
C
D
If a parabola opens upward, then there is a minimum value. If a parabola opens
downward, then there is a maximum value.
The maximum or minimum value is the y-value of the vertex.
Correct!
The maximum or minimum value is the y-value of the vertex.
PTS: 1
DIF: Average
REF: Page 592
OBJ: 9-1.4 Identifying the Vertex and the Minimum or Maximum
NAT: 12.5.4.c
STA: A.G.10
TOP: 9-1 Identifying Quadratic Functions
2
Name: ________________________ Class: ___________________ Date: __________
ID: C
Quadratic Exploration Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the axis of symmetry of the graph of y = 3x 2 + 6x + 4 .
a. x = −1
b. x = 1
c. y = 1
d. y = −1
____
2. Tell whether the graph of the quadratic function y = 9x 2 − 7x + 3 opens upward or downward. Explain.
a. Because a < 0, the parabola opens downward.
b. Because a > 0, the parabola opens downward.
c. Because a < 0, the parabola opens upward.
d. Because a > 0, the parabola opens upward.
____
3. Identify the vertex of the parabola. Then give the minimum or maximum value of the function.
a.
b.
c.
d.
The vertex is (5, − 6), and the minimum is –6.
The vertex is (5, − 6), and the maximum is 5.
The vertex is (5, − 6), and the maximum is –6.
The vertex is (5, − 6), and the minimum is 5.
1
Name: ________________________
____
ID: C
4. A swim team member performs a dive from a 14-foot-high springboard. The parabola below shows the path
of her dive.
Which equation represents the axis of symmetry?
a. y = 3
c.
b. x = 23
d.
2
y = 23
x=3
ID: C
Quadratic Exploration Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: A
b
For a quadratic function y = ax 2 + bx + c , the axis of symmetry is the vertical line x = − 2a .
y = 3x 2 + 6x + 4
a = 3, b = 6
b
6
x = − 2a = − 2(3) = −1
Find the values of a and b.
Substitute the values into the formula.
Feedback
A
B
C
D
Correct!
Use the formula x = -b/2a to find the axis of symmetry.
Use the formula x = -b/2a to find the axis of symmetry.
The axis of symmetry of a parabola is a vertical line. All the points it contains have the
same x-value, so the variable in the equation should be x and not y.
PTS: 1
DIF: Average
REF: Page 601
OBJ: 9-2.3 Finding the Axis of Symmetry by Using the Formula
NAT: 12.5.1.e
STA: A.A.41
TOP: 9-2 Characteristics of Quadratic Functions
2. ANS: D
Check that the function is in standard form.
y = 9x 2 − 7x + 3
a=9
Identify the value of a.
Since a > 0, the parabola opens upward.
Feedback
A
B
C
D
If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.
If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.
To determine the direction the parabola opens, find the value of a in the standard form
of the equation.
Correct!
PTS: 1
DIF: Average
REF: Page 592
OBJ: 9-1.3 Identifying the Direction of a Parabola
NAT: 12.5.1.e
STA: 8.G.21
TOP: 9-1 Identifying Quadratic Functions
1
ID: C
3. ANS: A
The vertex is the highest or lowest point on the parabola. If a parabola opens upward, the vertex is the lowest
point. If a parabola opens downward, the vertex is the highest point. The maximum or minimum value is the
y-value of the vertex.
Feedback
A
B
C
D
Correct!
If a parabola opens upward, then there is a minimum value. If a parabola opens
downward, then there is a maximum value.
The maximum or minimum value is the y-value of the vertex.
The maximum or minimum value is the y-value of the vertex.
PTS:
OBJ:
NAT:
4. ANS:
TOP:
1
DIF: Average
REF: Page 592
9-1.4 Identifying the Vertex and the Minimum or Maximum
12.5.4.c
STA: A.G.10
TOP: 9-1 Identifying Quadratic Functions
D
PTS: 2
REF: 080813ia
STA: A.G.10
Identifying the Vertex of a Quadratic Given Graph
2