Math
Spring Operational 2015
Algebra 2
PBA Item #11
How Work Contributes
VH029260
Prompt
Task is worth a total of 4 points.
VH029260 Rubric Part A
Score Description
1
Student response includes the following element.
•
0
This is machine-scored.
Student response is incorrect or irrelevant.
VH029260 Rubric Part B
Score Description
3
Student response includes the following 3 elements.
•
Reasoning component = 3 point
o
o
o
The equation is correctly rewritten in factored form and the key
feature is correctly explained.
The equation is correctly rewritten by completing the square and
the key feature is correctly explained.
f (0) is correctly evaluated and the key feature is correctly
explained.
Sample Student Response:
Student reasons that Angela has factored the expression in order to find the xintercepts of the function.
2
f ( x ) = 4x + 8x − 5
f ( x ) =(2x − 1)(2x + 5)
If the function is set equal to 0, then
0 =(2x − 1)(2x + 5)
x + 5
=
2x − 1
0 and 2
=
1
2
x
=
=
and x
0
−5
2




Therefore the x-intercepts are  1 , 0  and  − 5 , 0  .
 2

2

Student reasons that Benjamin completes the square on the function in order
to find the vertex.
f (x) =
f (x) =
4x
2
4( x
2
2
+ 8x − 5
+ 2x ) − 5
f ( x=
)
4( x
+ 2x + 1) − 5 − 4
f (x) =
4( x + 1)
2
− 9
Therefore the vertex is (−1, −9).
Student reasons that Carla evaluates f (0) to find the y-intercept at (0, −5).
Note: The response does not need to find the value of the key feature in order
to identify the key feature.
2
Student response includes 2 of the 3 elements.
1
Student response includes 1 of the 3 elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A8
A1
Part B: Score Point 3
Annotations
Anchor Paper 1
Part B: Score Point 3
This response receives full credit. The student includes each of the three required elements:
•
[Angella] The student rewrites the equation in factored form (𝑓(𝑥) = (2𝑥 − 1)(2𝑥 +
5)) and describes the x-intercepts (Angella’s work can be used to find the x-intercepts
by using the zero product property) [this additional information is true and does not
change the score].
•
[Benjamin] The student completes the square (𝑓(𝑥) = 4(𝑥 + 1)2 − 9) and describes the
vertex (Benjamin’s work will find the vertex, orintation, and strech factor from the
b,h,and a values) [this additional information is true and does not change the score].
•
[Carla] The student evaluates f(0) (𝑓(0) = −5) and describes the y-intercept (Carla’s
work yeilds the y-intercept of the parabola).
The response also correctly shows the x-intercepts and vertex. These values are ignored and
are not considered in scoring the response.
While supporting calculations are shown for all three students, it is not necessary for credit;
only the factored form/completed square/y-intercept and the descriptions of the key features
are required.
The graph is computer-scored and will not be considered when scoring the response.
A2
Part B: Score Point 3
Annotations
Anchor Paper 2
Part B: Score Point 3
This response receives full credit. The student includes each of the three required elements:
•
[Angella] The student rewrites the equation in factored form (𝑓(𝑥) = (2𝑥 − 1)(2𝑥 + 5))
and describes the x-intercepts (Angella finds the x intercepts of the equation).
•
[Benjamin] The student completes the square (𝑓(𝑥) = 4(𝑥 + 1)2 − 9) and describes the
vertex (Benjamin finds the vertex).
•
[Carla] The student evaluates f(0) (𝑓(0) = −5) and describes the y-intercept (Carla
finds the y intercept).
The response also correctly shows the x-intercepts and vertex. These values are ignored and
are not considered in scoring the response.
A3
Part B: Score Point 2
Annotations
Anchor Paper 3
Part B: Score Point 2
This response receives partial credit. The student includes two of the three required
elements:
•
[Benjamin] The student completes the square (𝑓(𝑥) = 4(𝑥 + 1)2 − 9) and describes the
vertex (Benjamin completes the square . . . so he can find the vertex).
•
[Carla] The student evaluates f(0) by giving the coordinates of the y-intercept ((0, −5))
and describes the y-intercept (Carla evaluates it for f(0) so she can find the yintercept).
The response also correctly shows the x-intercepts, vertex, and y-intercept. These values are
ignored and are not considered in scoring the response.
No credit is given for Angella; while the explanation of the key feature is correct (Angella
factors it . . . to show where the line intercepts the x-axis) the equation is rewritten
incorrectly (𝑓(𝑥) = (𝑥 − .5)(𝑥 + 2.5)) is equivalent to 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 1.25; it is missing a factor of
4.
A4
Part B: Score Point 2
Annotations
Anchor Paper 4
Part B: Score Point 2
This response receives partial credit. The student includes two of the three required
elements:
•
[Angella] The student rewrites the right side of the equation in factored form
((2𝑥 − 1)(2𝑥 + 5)) and describes the x-intercepts (Zeroes).
•
[Carla] The student evaluates f(0) (𝑓(0) = −5) and describes the y-intercept (yintercept).
No work or explanation are presented for Benjamin.
A5
Part B: Score Point 1
Annotations
Anchor Paper 5
Part B: Score Point 1
This response receives partial credit. The student includes one of the three required
elements:
•
[Angella] The student rewrites the right side of the equation in factored form
((2𝑥 + 5)(2𝑥 − 1)) and describes the x-intercepts (Each student work contributes to
finding the x intercepts).
No credit is given for Benjamin; the response has not completed the square and the
description of the vertex (Each student work contributes to finding the x intercepts) is
incorrect.
No credit is given for Carla; while f(0) has been evaluated correctly (Carla would find −5), the
description of the y-intercept (Each student work contributes to finding the x intercepts) is
incorrect. Even if the y-intercept were described correctly, the additional incorrect information
would keep the response from being credited.
A6
Part B: Score Point 1
Annotations
Anchor Paper 6
Part B: Score Point 1
This response receives partial credit. The student includes one of the three required
elements:
•
[Carla] The student evaluates f(0) by giving the coordinates of the y-intercept ((0, −5))
and describes the y-intercept (Carla finds the y intercept when she plugs 0 in for x).
The response correctly shows the x-intercepts and vertex. These values are ignored and are
not considered in scoring the response.
No credit is given for Angella; while the explanation of the key feature is correct (When
Angella factors the function she finds the zeros), the equation was not rewritten in factored
form.
No credit is given for Benjamin; while the explanation of the key feature is correct (Benjamin
finds the vertex to use when graphing the function by completing the square), the response
has not correctly completed the square.
A7
Part B: Score Point 0
Annotations
Anchor Paper 7
Part B: Score Point 0
This response receives no credit. The student includes none of the three required elements.
No credit is given for Angella; while the right side of the equation is factored correctly
((2𝑥 + 5)(2𝑥 − 1)), the x-intercepts are not described.
No credit is given for Benjamin; the response has not correctly completed the square
(4(𝑥 − 7)2 + 1) and the vertex is not described.
No credit is given for Carla; while f(0) is evaluated correctly (−5), the y-intercept is not
described.
A8
Part B: Score Point 0
Annotations
Anchor Paper 8
Part B: Score Point 0
This response receives no credit. The student includes none of the three required elements.
No work or explanation are presented for Angella.
No work or explanation are presented for Benjamin.
No credit is given for Carla; while f(0) is evaluated correctly (𝑓(0) = −5), the description of the
y-intercept is incorrect (key features that are revealed are the y-intercept and the slope of
the line) [(slope) is incorrect for any of the features]. The addition of an incorrect term
makes the entire description incorrect.
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
3
P102
2
P103
1
P104
0
P105
2