2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 1 Honors
Approximate Time:
4 Days
Module 19: Graphing Quadratic Functions
Learning Goal
The student is expected to understand and
recognize a quadratic function in either vertex or
standard form. The student is also expected to
perform transformations on quadratic functions and
their graphs.
Essential Questions
1.
2.
3.
4.
How can you use the graph of a quadratic function to
solve real-world problems?
What is the effect of the constant a on the graph of
𝑓(𝑥) = 𝑎𝑥 2
How can you obtain the graph of 𝑔(𝑥) = 𝑎(𝑥 − ℎ)2 +
𝑘 from the graph of 𝑓(𝑥) = 𝑥 2
How can you change the vertex form of a quadratic
function to standard form?
Unit Overview
This unit extends the students understanding of functions to
include quadratic functions. The student will apply skills gained in
their study of linear and piecewise functions, such as graphing
and performing transformations. The unit also discusses the
forms of a quadratic function, such as vertex form and standard
form. .
Vertical Progression
MAFS.8.EE.1.1, MAFS.8.NS.1.1: In Grade 8 students worked with expressions involving square and cube roots, irrational numbers and expressions with integer exponents and worked
with expressions and equations for real life problems.
Module Focus Standards
Module Topics
Algebra 1 Test Item Specs (Reference Sheet at End)
High School Flipbook
MAFS.912.F-BF.2.3: (DOK 2) 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. (conceptual, procedural)
 Given a single transformation on a symbolic or graphic function, identify the
effect on the graph.
 Using technology, identify effects of single transformations on graphs of
functions.
 Graph a given function by 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).
 Describe the differences and similarities between a parent function and the
transformed function.
 Find the value of k, given the graphs of a parent function, f(x), and the
transformed function: f(x) + k, k f(x), f(kx), or f(x + k).
 Recognize even and odd functions from their graphs and equations.
 Experiment with cases and illustrate an explanation of the effects on the
graph, using technology.
Understanding Quadratic Functions (F-BF.2.3, FIF.1.2, F-IF.2.4, F-IF.3.7a)
Resources:
 Lesson 19.1 (HMH Book)
 Module 4 Lesson 8 – Engage NY
Formative Assessments:
 Lesson Performance Task (HMH pg. 902)
 Elevation Along a Trail - CPALMS
 Properties of Parabolas - Kuta
Transforming Quadratic Functions (F-BF.2.3, FBF.1.1, F-IF.2.4, F-IF.1.2)
Resources:
 Lesson 19.2 (HMH Book)
 Module 4 Lesson 21 – Engage NY
Formative Assessments:
 Lesson Performance Task (HMH pg. 916)
 Comparing Functions – Quadratics – CPALMS
Essential Vocabulary










quadratic function
parabola
vertex
axis of symmetry
minimum value
maximum value
vertical translation
horizontal translation
vertex form
standard form
Higher Order Question Stems
 What do the numbers or symbols used in the
problem represent?
 What would happen if . . . ?
Writing Connections
 Write a contextual problem that the
equation/expression could represent.
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 1 Honors
4 Days
Module 19: Graphing Quadratic Functions
MAFS.912.F-IF.1.2: (DOK 2) Use function notation, evaluate functions for inputs
in their domains, and interpret statements that use function notation in terms
of a context. (conceptual, procedural)
 Identify mathematical relationships and express using function notation.
 Define a reasonable domain, which depends on the context and/or
mathematical situation, for a function focusing on linear and exponential
functions.
 Evaluate functions at a given input in the domain, focusing on linear and
exponential functions.
 Interpret statements that use functions in terms of real world situations,
focusing on linear and exponential functions.
MAFS.912.F-IF.2.4: (DOK 2) 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. Key features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative maximums and minimums;
symmetries; end behavior; and periodicity. (conceptual)
 Define and recognize the key features in tables and graphs of linear and
exponential functions: intercepts; intervals where the function is increasing,
decreasing, positive, or negative, and end behavior.
 Interpret key features of graphs and tables of functions in the terms of the
contextual quantities each function represents.
 Sketch graphs showing the key features of a function, modeling a relationship
between two quantities, given a verbal description of the relationship.
MAFS.912.F-IF.3.7a: (DOK 2) 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. (conceptual, procedural) Quick Reference
Sheet
 Graph linear functions by hand in simple cases or using technology for more
complicated cases and show/label intercepts of the graph.
 Determine the differences between simple and complicated linear,
exponential and quadratic functions and know when the use of technology is
appropriate.
Interpreting Vertex Form and Standard Form (FIF.2.4, F-IF.3.8, F-IF.1.2, F-IF.2.4, F-BF.1.1)
Resources:
 Lesson 19.3 (HMH Book)
 Module 4 Lesson 16 – Engage NY
 Module 4 Lesson 17 – Engage NY
Formative Assessments:
 Lesson Performance Task (HMH pg. 930)
 Vertex Form of Parabolas - Kuta
Approximate Time:
 Write to explain the connections made
between prior knowledge and new content.
Link to Webb’s DOK Guide
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 1 Honors
Module 19: Graphing Quadratic Functions
MAFS.912.F-BF.1.1: (DOK 3) Write a function that describes a relationship
between two quantities. (a) Determine an explicit expression, a recursive
process, or steps for calculation from a context. (conceptual, application)
 Define explicit function and recursive process.
 Write a function that describes a relationship between two quantities by
determining an explicit expression, a recursive process, or steps for
calculation from a context.
(b) Combine standard function types using arithmetic operations. For example,
build a function that models the temperature of a cooling body by adding a
constant function to a decaying exponential, and relate these functions to the
model. (conceptual, procedural, application)
 Combine two functions using the operations of addition, subtraction,
multiplication, and division.
 Evaluate the domain of the combined function.
 Given a real-world situation or mathematical problem, build standard
functions to represent relevant relationships/ quantities.
 Given a real-world situation or mathematical problem, determine which
arithmetic operation should be performed to build the appropriate combined
function.
(c) Compose functions. For example, if T(y) is the temperature in the
atmosphere as a function of height, and h(t) is the height of a weather balloon
as a function of time, then T(h(t)) is the temperature at the location of the
weather balloon as a function of time. (conceptual, application)
 Given a real-world situation or mathematical problem, relate the combined
function to the context of the problem.
 Compose functions.
MAFS.912.F-IF.3.8: (DOK 2) 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. (conceptual, procedural)
 Identify different forms of a quadratic expression.
 Identify zeros, extreme values, and symmetry of the graph of a quadratic
function.
 Identify how key features of a quadratic function relate to its characteristics
in a real-world context.
 Write functions in equivalent forms using the process of factoring.
Approximate Time:
4 Days
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 1 Honors
Module 19: Graphing Quadratic Functions
 Interpret different yet equivalent forms of a function defined by an
expression in terms of a context.
 Given the expression of a quadratic function, interpret zeros, extreme
values, and symmetry of the graph in terms of a real-world context.
 Write a quadratic function defined by an expression in different but
equivalent forms to reveal and explain different properties of the function
and determine which form of the quadratic is the most appropriate for
showing zeros and symmetry of a graph in terms of a real-world context.
 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.
(b) Use the properties of exponents to interpret expressions for exponential
functions. (conceptual)
 Classify the exponential function as exponential growth or decay by
examining the base.
 Identify how key features of an exponential function relate to its
characteristics in a real-world context.
 Use the properties of exponents to interpret expressions for exponential
functions in a real-world context.
 Given the expression of an exponential function, interpret the expression in
terms of a real-world context, using the properties of exponents.
 Write an exponential function defined by an expression in different but
equivalent forms to reveal and explain different properties of the function,
and determine which form of the function is the most appropriate for
interpretation in a real-world context.
Mathematical Practices
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.2.1: Reason abstractly and quantitatively
MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning.
Approximate Time:
4 Days