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Algebra 2 | Unit B: Quadratic Functions
Unit Overview
Major Focus: Students will understand the various properties of quadratic functions and will use quadratic functions to
model real-world phenomena.
Tasks:

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Identify key features of quadratic functions such as vertex (max/min), intercepts (including zeroes), focus, and
directrix, and use those features to sketch a graph.
Solve quadratic equations by using inspection, taking square roots, completing the square, factoring, and using
the quadratic formula.
Model real-world phenomena using quadratic functions.
Solve systems of equations that include a quadratic equation.
Perform operations with complex numbers and solve quadratic equations that have complex solutions.
Compare properties of functions that are represented differently (i.e. algebraically and graphically).
Textbook Resources
Mathematics Formative Assessment System Tasks
Pearson Prentice Hall Algebra 2 copyright 2011
Sections: 4-1, 4-2, CC1, CC2, 4-5, 4-6, CC3, 4-7, 4-8, CC4
The system includes tasks or problems that teachers can
implement with their students, and rubrics that help the
teacher interpret students' responses. Teachers using
MFAS ask students to perform mathematical tasks, explain
their reasoning, and justify their solutions. Rubrics for
interpreting and evaluating student responses are included
so that teachers can differentiate instruction based on
students' strategies instead of relying solely on correct or
incorrect answers. The objective is to understand student
thinking so that teaching can be adapted to improve
student achievement of mathematical goals related to the
standards. Like all formative assessment, MFAS is a
process rather than a test. Research suggests that welldesigned and implemented formative assessment is an
effective strategy for enhancing student learning.
http://www.cpalms.org/resource/mfas.aspx
MUST ADD: Algebra 2 Common Core Additional
Lessons:
CC-1: Equation of a Parabola (using focus and directrix)
CC-2: Modeling with Quadratic Functions
CC-3: Quadratic Expressions and Functions (Graphing by
Factoring and Completing the Square)
CC-4: Systems of Linear and Quadratic Equations
Available under Teacher Resources of the Algebra 2
content at www.pearsonsuccessnet.com.
Section to consider for remediation: 4-4
This a working document that will continue to be revised and improved taking your feedback into consideration.
Math Florida Standards
Content Standards
(bold are directly
assessed)
MAFS.912.A-REI.2.4
MAFS.912.A-REI.3.7
MAFS.912.A-SSE.2.3a,b
MAFS.912.F-BF.2.3
MAFS.912.F-IF.3.7a
MAFS.912.F-IF.3.8a
MAFS.912.F-IF.3.9
MAFS.912.G-GPE.1.2
MAFS.912.N-CN.1.1
MAFS.912.N-CN.1.2
MAFS.912.N-CN.3.7
Standards for
Mathematical Practice
MAFS.K12.MP.2.1
MAFS.K12.MP.7.1
Other Resources
Kuta Software
Purple Math
Algebra Nation
Online Graphing Calculator
National Library of Virtual Manipulatives
Geogebra
Virtual Nerd
YouTube
Khan Academy—Math
Engage NY
TI Nspired Resource Center for Educators
Pasco County Schools, 2014-2015
Algebra 2 | Unit B: Quadratic Functions
Tasks: Interactive Digital Paths and Dynamic Activities – Pearson Online
a. section 4-1 Quadratic Functions and Transformations Pearson Prentice online text teacher resources digital path  dynamic activity allows manipulation of h, k
and a to yield various changes in the graph
b. section 4-2 Standard form of a Quadratic Function Pearson Prentice online text teacher resources digital path  dynamic activity allows manipulation of a, b and c
when the equation is in polynomial form
c. section 4-4 Factoring Quadratic Expressions Pearson Prentice online text teacher resources digital path  dynamic activity allows one to model then factor the
polynomial
d. section 4-5 Quadratic Equaitons Pearson Prentice online text teacher resources digital path  2nd dynamic activity allows one to model then factor the polynomial
that has a>2
e. section 4-5 Quadratic Equations Pearson Prentice online text teacher resources digital path  dynamic activity allows one to graph the factored form the quadratic
and observe how changes in a, r1 and r2 affect the graph
f. section 4-6 Completing the Square Pearson Prentice online text teacher resources digital path  dynamic activity allows one to complete the square with electronic
Algeblocks
g. section 4-7 Quadratic Formula Pearson Prentice online text teacher resources digital path  dynamic activity allows one change a, b and c on the quadratic to give
a visual of how that affects the zeros of the equation.
Glencoe McGraw-Hill “Precalculus” copyright 2011 student Study Notebook sections 7-1 and 7-2
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit B: Quadratic Functions
Unit Scale (Multidimensional) (MDS)
The multidimensional, unit scale is a curricular organizer for PLCs to use to begin unpacking the unit. The MDS should not be used directly with students and is not for
measurement purposes. This is not a scoring rubric. Since the MDS provides a preliminary unpacking of each focus standard, it should prompt PLCs to further explore question #1,
“What do we expect all students to learn?” Notice that all standards are placed at a 3.0 on the scale, regardless of their complexity. A 4.0 extends beyond 3.0 content and helps
students to acquire deeper understanding/thinking at a higher taxonomy level than represented in the standard (3.0). It is important to note that a level 4.0 is not a goal for the
academically advanced, but rather a goal for ALL students to work toward. A 2.0 on the scale represents a “lightly” unpacked explanation of what is needed, procedural and
declarative knowledge i.e. key vocabulary, to move students towards proficiency of the standards.
4.0
In addition to displaying a 3.0 performance, the student must demonstrate in-depth inferences and applications that go beyond what was taught within these
standards. Examples:

3.0
Given a modeling context resulting in a system of quadratic equations, solve a system of quadratic equations with up to 4 solutions, interpret the results,
and determine which solutions are viable for the problem.
The Student will:
 Solve quadratic equations in one variable.
o Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions.
Derive the quadratic formula from this form.
o Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as
appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers
a and b. (MAFS.912.A-REI.2.4)
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Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. (MAFS.912.A-REI.3.7)
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
o Factor a quadratic expression to reveal the zeros of the function it defines.
o Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. (MAFS.912.A-SSE.2.3)
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given
the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from
their graphs and algebraic expressions for them. (MAFS.912.F-BF.2.3)
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
o Graph linear and quadratic functions and show intercepts, maxima, and minima. (MAFS.912.F-IF.3.7a)
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
o Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret
these in terms of a context. (MAFS.912.F-IF.3.8a)

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example,
given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. (MAFS.912.F-IF.3.9)
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Derive the equation of a parabola given a focus and directrix. (MAFS.912.G-GPE.1.2)
Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real. (MAFS.912.N-CN.1.1)
Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. (MAFS.912.N-CN.1.2)
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit B: Quadratic Functions

2.0
Solve quadratic equations with real coefficients that have complex solutions. (MAFS.912.N-CN.3.7)
The student will recognize or recall specific vocabulary, such as:
Key vocabulary: completing the square, square root, quadratic formula, factor, vertex form, standard form, maximum, minimum, intercepts, zeroes,
extreme values, symmetry, parabola, focus, directrix, complex number
The student will perform basic processes, such as:
 Identify the best solution method given a quadratic equation
 Determine whether a given solution satisfies a given system of equations (including one quadratic)
 Rewrite perfect square trinomials
 Translate functions on a graph given a verbal description
 Find the vertex of a parabola given a quadratic equation in standard form
 Factor simple trinomials
 Compare two functions that are represented using the same way (i.e. both are graphs)
 Find the focus of a parabola.
 Add and subtract complex numbers
1.0
With help, partial success at 2.0 content but not at score 3.0 content
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit B: Quadratic Functions
Unpacking the Standard: What do we want students to Know, Understand and Do (KUD):
The purpose of creating a Know, Understand, and Do Map (KUD) is to further the unwrapping of a standard beyond what the MDS provides and assist PLCs in answering question
#1, “What do we expect all students to learn?” It is important for PLCs to study the focus standards in the unit to ensure that all members have a mutual understanding of what
student learning will look and sound like when the standards are achieved. Additionally, collectively unwrapping the standard will help with the creation of the uni-dimensional
scale (for use with students). When creating a KUD, it is important to consider the standard under study within a K-12 progression and identify the prerequisite skills that are
essential for mastery.
Domain: Algebra: Reasoning with Equations & Inequalities
Cluster: Solve equations and inequalities in one variable. (Supporting)
Standard: MAFS.912.A-REI.2.4: (Solve) quadratic equations in one variable.
Understand
“Essential understandings,” or generalizations, represent ideas that are transferable to other contexts.
Understand that there are two solutions to every quadratic equation, that the solutions may or may not be unique and may or may not be real, and that the solutions are
always obtainable using either factoring, completing the square, or the quadratic formula.
Know
Declarative knowledge: Facts, vocab., information
Vocab: Quadratic equations, solutions to
quadratic equations
Do
Procedural knowledge: Skills, strategies and processes that are transferrable to other contexts.
Solve quadratic equations in one variable.
Prerequisite skills: What prior knowledge (foundational skills) do students need to have mastered to be successful with this standard?
Using the addition and multiplication properties of equality, factoring trinomials, completing the square, using the quadratic formula, simplifying radicals, using complex
numbers
Learning Goals:
Students will solve quadratic equations in one variable.
Moving Beyond:
In Pre-calculus, a deep understanding of parabolas will aid students in their understanding of all conics.
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit B: Quadratic Functions
Uni-Dimensional, Lesson Scale:
The uni-dimensional, lesson scale unwraps the cognitive complexity of a focus standard for the unit, using student friendly language. The purpose is to articulate distinct levels of
knowledge and skills relative to a specific topic and provide a roadmap for designing instruction that reflects a progression of learning. The sample performance scale shown
below is just one example for PLCs to use as a springboard when creating their own scales for student-owned progress monitoring. The lesson scale should prompt teams to
further explore question #2, “How will we know if and when they’ve learned it?” for each of the focus standards in the unit and make connections to Design Question 1,
“Communicating Learning Goals and Feedback” (Domain 1: Classroom Strategies and Behaviors). Keep in mind that a 3.0 on the scale indicates proficiency and includes the
actual standard. A level 4.0 extends the learning to a higher cognitive level. Like the multidimensional scale, the goal is for all students to strive for that higher cognitive level,
not just the academically advanced. A level 2.0 outlines the basic declarative and procedural knowledge that is necessary to build towards the standard.
MAFS.912.A-REI.2.4: Solve quadratic equations in one variable.
Score
4.0
3.5
Learning Progression
2.0
1.0
+ bx + c = 0, derive the quadratic equation by
I can…
 Derive the quadratic equation by completing the square.
1. Given the equation ax
completing the square.
I can do everything at a 3.0, and I can demonstrate partial success at score 4.0.
I can…
 Solve quadratic equations in one variable.
1. Solve:
3x 2 + 7x -10 = 0
2. Solve:
x 2 - 5x + 3 = 0
3.0
2.5
Sample Tasks
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0.
I can…
 Complete the square
 Factor a quadratic trinomial
 Substitute the coefficients of quadratic equations into the quadratic
formula
2
1. Rewrite the following equation so that it contains a perfect square:
x 2 -12x = 6
2. Factor the following trinomial: 2x -13x - 7
3. Substitute the coefficients of the following equation into the quadratic
2
formula: 3x - 4x -15 = 0
2
I need prompting and/or support to complete 2.0 tasks.
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 2 | Unit B: Quadratic Functions
Sample High Cognitive Demand Tasks:
These task/guiding questions are intended to serve as a starting point, not an exhaustive list, for the PLC and are not intended to be prescriptive. Tasks/guiding questions simply
demonstrate one way to help students learn the skills described in the standards. Teachers can select from among them, modify them to meet their students’ needs, or use them
as an inspiration for making their own. They are designed to generate evidence of student understanding and give teachers ideas for developing their own activities/tasks and
common formative assessments. These guiding questions should prompt the PLC to begin to explore question #3, “How will we design learning experiences for our students?”
and make connections to Marzano’s Design Question 2, “Helping Students Interact with New Knowledge”, Design Question 3, “Helping Students Practice and Deepen New
Knowledge”, and Design Question 4, “Helping Students Generate and Test Hypotheses” (Domain 1: Classroom Strategies and Behaviors).
CCSS Mathematical Content Standard(s)
MAFS.912.A-REI.2.4: Solve quadratic equations in one variable.
Design Question 1; Element 1
CCSS Mathematical Practice(s)
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
MAFS.K12.MP.7.1: Look for and make use of structure.
Design Question 1; Element 1
Marzano’s Taxonomy
Level 4—Knowledge Utilization: “Experimenting”
Questions:
What would h(0) represent?
Can you defend your answer with mathematical reasoning?
Which part of the parabola (intercept, vertex, etc.) would this question relate to?
Misconceptions:
Incorrect computations (order of operations)
Solving for the incorrect zero.
Differentiation:
Shift the diving board higher and lower for extending students.
Have step-by-step instructions for struggling students.
Suppose h(t) = −5t2 + 10t + 3 is an expression giving the height of a diver above the water (in meters), t seconds after the
diver leaves the springboard.
Teacher Notes
Task
a.
A. How high above the water is the springboard? Explain how you know.
b.
B. When does the diver hit the water?
c.
C. At what time on the diver's descent toward the water is the diver again at the same height as the springboard?
d.
D. When does the diver reach the peak of the dive?
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015