Progressive Mathematics Initiative
www.njctl.org
Mathematics Curriculum
Unit Plan # 3
Title: Quadratics
Subject: Algebra 2
Length of Time: 3 weeks
Unit Summary: The unit covers quadratic equations. Students learn to graph quadratic functions and find
the zeros of the function through graphing, factoring, square roots, completing the square, and the quadratic
formula. The standard form of quadratics and graphing quadratic inequalities will also be discussed.
Learning Targets
Conceptual Category: Algebra Domain: Seeing Structure in Expressions
Cluster: Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it. For example, see x4 –
A-SSE.2
y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as
(x2 – y2)(x2 + y2).
Cluster: Write expressions in equivalent forms to solve problems
A-SSE-3
Choose and produce an equivalent form of an expression to reveal and explain properties
of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or
minimum value of the function it defines.
Conceptual Category: Algebra Domain: Arithmetic with Polynomials & Rational Expressions
Cluster: Understand the relationship between zeros and factors of polynomials
A-APR.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros
to construct a rough graph of the function defined by the polynomial.
Conceptual Category: Algebra Domain: Creating Equations
Cluster: Create equations that describe numbers or relationships
A-CED.1
Create equations and inequalities in one variable and use them to solve problems.
Conceptual Category: Algebra Domain: Reasoning with Equations & Inequalities
Cluster: Solve equations and inequalities in one variable
A-REI.4
Solve quadratic equations in one variable.
Cluster: Represent and solve equations and inequalities graphically
A-REI.10
Understand that the graph of an equation in two variables is the set of all its solutions
plotted in the coordinate plane, often forming a curve (which could be a line).
Conceptual Category: Functions Domain: Interpreting Functions
Cluster: Interpret functions that arise in applications in terms of the context
F-IF.4
For a function that models a relationship between two quantities, interpret key features of
graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description
of the relationship.
F-IF.5
Relate the domain of a function to its graph and, where applicable, to the quantitative
relationship it describes.
Cluster: Analyze functions using different representations
F-IF.7
Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Algebra II – Quadratics
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F-IF.8
Write a function defined by an expression in different but equivalent forms to reveal and
explain different properties of the function.
a. 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.
F-IF.9
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.
Conceptual Category: Functions Domain: Building Functions
Cluster: Build new functions from existing functions
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),f(kx), and f(x + k) for
F-BF.3
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.
Conceptual Category: Geometry Domain: Expressing Geometric Properties with Equations
Cluster: Translate between the geometric description and the equation for a conic sections
G-GPE.2
Derive the equation of a parabola given a focus and directrix.
Unit Essential Question:
Unit Enduring Understandings:
 How can we find the position of an object at a
 The graph of a quadratic is U-shaped and
given time, including when it hits the ground?
called a parabola.
 A quadratic can have 0, 1, or 2 zeros.
 How are quadratic functions used to model,
 The x-intercepts of a quadratic can also be
analyze and interpret mathematical relationships?
called zeros or solutions.
 What are the advantages of a quadratic function in

To find the zeros of a quadratic function, you
vertex form? In standard form?
must set the equation equal to zero.
 The quadratic formula can be used to find
zeros.
 The discriminant of a quadratic formula can tell
the number and nature of the roots.
 Completing a perfect square trinomial allows
you to factor the completed trinomial as the
square of a binomial.
 In the graph of 𝑓(𝑥) = 𝑎(𝑏(𝑥 + 𝑐))2 + 𝑑, a is a
vertical dilation or reflection, b is a horizontal
dilation or reflection, c is a horizontal slide, and
d is a vertical slide of 𝑓(𝑥) = 𝑥 2 .
Unit Objectives:
 Students will be able to understand and graph key features of quadratic equations.
 Students will be able to solve quadratic equations graphically and algebraically (factoring, square
roots, completing the square, and using the quadratic formula).
 Students will be able to state the number and nature of the roots of a quadratic using the
discriminant.
 Students will be able to apply the techniques for finding zeros of a quadratic to real-world problems.
Evidence of Learning
Formative Assessments:
 SMART Response questions used throughout the unit.
 6 Quizzes
Summative Assessment:
 Unit Test
Algebra II – Quadratics
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Lesson Plan
Topics
Timeframe (days)
Topic #1: Key terms, Identify Quadratic Functions,
and Explain Characteristics
Topic #2: Combining Transformations
Topic #3: Graph Quadratic Functions
Quiz 1 Quadratic Functions
Topic #4: Solve Quadratic Functions: Graphically
Quiz 2 Solve Quadratics by Graphing
Topic #5: Solve Quadratic Functions: Factoring
Topic #6: Application of the Zero Product Property
Topic #7: Solve Quadratic Functions: Square Roots
Topic #8: Solve Quadratic Functions: Completing
the Square
Quiz 3 Solve Quadratics Algebraically
Topic #9: Solve Quadratic Functions: Quadratic
Formula
Topic #10: The Discriminant
Quiz 4 Discriminant/Quadratic Formula
Topic #11: Vertex and Standard Form
Quiz 5 Vertex and Standard Form
Topic #12: More Application Problems
Lab: Roller Coaster
Quiz 6 Application of Quadratics
Review and Unit Test
Curriculum Resources:
 www.njctl.org/courses/math/algebra2/
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