PUSD Math News – Mathematics 2
Module 1: Quadratic Functions
Module 1 Overview – Quadratic
Functions
(Standards: F.BF.1, A.SSE.1, A.CED.2, F.LE.1,
F.LE.2, F.LE.3)
Student and Teacher materials can be found
at Mathematics Vision Project
http://www.mathematicsvisionproject.org/
(Curriculum>Secondary Mathematics
Two>Module 1: Quadratic Functions)
In Module 1 students deepen their understanding
of linear and exponential functions learned in
Mathematics 1 by relating what they know about
features of functions and applying that
understanding to quadratic functions. Students
further develop their understanding of quadratic
functions by distinguishing between patterns that
are quadratic, linear, exponential or neither. They
examine and analyze these relationships using
multiple representations including tables, graphs,
equations, visuals, and story context.
Module 1 further develops students’ proficiency in
the Standards of Mathematical Practice. This
module focuses on MP1 and MP6, as these are
umbrella standards. In order to successfully
engage in a task, students must first make sense of
it. Students should make sense of the real world
use of quadratic, linear, and exponential functions.
Students also explore MP4, as they are required to
decide which of several types of models is most
reasonable in a real-world situation. After
deciding, students must use data to specify the
parameters in the model. Once the model is
specified, students must use the model to solve a
problem about the situation. Students also have
several choices of tools to use, for example a
scientific calculator and a plotter, to help develop
their work in MP5.
Scan the QR code below to take you
directly to the PUSD Secondary Math
Resources webpage for
Mathematics 2, Module 1: Quadratic
Functions
You will find the student text, newsletter;
standards for the module, homework help
links and more!
https://goo.gl/MUiumU
Vocabulary and Major Mathematical
Concepts
Note: Section numbers followed by an H will be
addressed in the Honors Mathematics 2 course.
Prerequisite Concepts and Skills:
 Graphing functions
 Identifying domain, range, and
intervals of increase and decrease
 Using patterns to find recursive and
explicit rules
 Using differences within a table of
values to determine the type of
function that can be used to
represent a data set
 Comparing features of functions
 Comparing linear and exponential
functions
 Finding multiple representations for a
context
PUSD Math News – Mathematics 2
Module 1: Quadratic Functions
Acceleration (1.5) – rate of change of velocity
per unit of time, generally it is an increase in the
rate or speed of something.
Area (1.2) – the amount of space, measured in
square units, contained within a flat, or plane
figure. The square units are usually a standard
unit, like a square meter, a square foot or a
square inch.
Imagehttps://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Shape_
Area.svg/400px-Shape_Area.svg.png
At rest (1.5) – not moving, a speed of zero.
Average rate of change (1.5) – the change in
the value of a quantity divided by the elapsed
time. For a function, this is the change in the yvalue divided by the change in the x-value for
two distinct points on the graph, or the slope of
the line segment that connects the two points.
Explicit equation (1.1) – a formula for a
sequence of numbers that allows us to find any
term in the sequence without knowing any other
terms.
Exponential function (1.1) – a mathematical
function of the form f(x)=ax where x is a variable,
and "a" is a constant called the base of the
function.
First & second differences (1.3) – when given a
sequence of numbers finding the first difference
means to find the differences between
consecutive terms in the sequence. Finding the
second differences means to find the difference
between consecutive first differences. Whenever
the second difference is constant in a sequence,
the sequence is said to be quadratic. See the
illustration below.
Example:
Image- http://mathematicsi.com/wp-content/uploads/quadraticsequences3.png
Average speed (1.5) – over a time interval,
average speed is the distance travelled by the
object divided by the duration of the interval.
Initial speed (1.5) – the speed of an object at
the beginning of an interval, an initial condition.
Binomial (1.2) – a polynomial with two terms
Instantaneous speed (1.5) – the speed of an
object at a particular moment.
2x+1
Examples:
3x2-4
6xy+5z
Domain (1.6) – the complete set of possible
values of the independent (x) variable. All
possible x-values for which the function “works”,
and gives an output of real y-values (see example
under range).
Interval notation (1.6) – a notation for
representing an interval as a pair of numbers.
The numbers are the endpoints of the interval.
Parentheses and/or brackets are used to show
whether the endpoints are excluded or included.
For example, [3, 8) is the interval of real
numbers between 3 and 8, including 3 and
excluding 8.
PUSD Math News – Mathematics 2
Module 1: Quadratic Functions
Maximum value (1.4) – the greatest value of a
function over its domain. For a quadratic
function there is a maximum value when the
parabola opens down. This maximum value
occurs at the vertex of a parabola.
Example:
Quadratic functions (1.4) – a second degree
(highest exponent on a variable is 2) polynomial
function written in the form y=ax2+bx+c. The
graph of a quadratic function is “u-shaped” and
called a parabola.
Range (1.6) – the complete set of all possible
resulting values of the dependent (y) variable,
after substituting the domain (all possible xvalues).
Example:
Imagehttp://www.asulearning.com/gradschool_courses/5642/mod_5/images/
max64.JPG
Minimum value (1.4) – the least value of a
function over its domain. For a quadratic
function there is a minimum value when the
parabola opens up. This minimum value occurs at
the vertex of a parabola.
Example:
Image- http://www.mathsisfun.com/sets/images/range-domaingraph.gif
Recursive equation (1.1) – a formula that
represents a sequence by describing the
relationship between its successive terms.
Main Topics
Note: Section numbers followed by an H will be
addressed in the Honors Mathematics 2 course.
Imagehttp://connectedmath.msu.edu/_connectedMath/assets/File/Families/I
mages/parabola.png
Parabola – the u-shaped curve that result when
a quadratic function is graphed.
Perimeter (1.2) – the total distance along the
edge of a figure.
Section in student text – Task done in class
Related Homework Help Videos
1.1 – An introduction to quadratic functions,
designed to elicit representations and surface
a new type of pattern of change
Distributive property
https://goo.gl/sZkyZ6
Quadratic sequences
https://goo.gl/mWRQkO
Imagehttp://www.mathematicsdictionary.com/english/vmd/images/p/perime
ter.gif
Linear, exponential or neither
https://goo.gl/3Pz7j8
PUSD Math News – Mathematics 2
Module 1: Quadratic Functions
1.1- cont’d
1.5- cont’d
Rate of change
https://goo.gl/XXDMed
Evaluating quadratic functions
https://goo.gl/vR1Ndd
1.2 – Examine quadratic patterns in multiple
representations and contrast with linear
patterns
Adding binomials
https://goo.gl/oGTywY
Perimeter and area of rectangles
https://goo.gl/hRDZHr
Greatest common factor
https://goo.gl/g0pStb
1.3 – Focus on nature of change between
values in a quadratic being linear
Multiplying binomials
https://goo.gl/sO6q8N
1.4 – Focus on maximum/minimum point as
well as domain and range for quadratics
Find slope given two points
https://goo.gl/fdjIaQ
Compare linear and exponential rates of change
https://goo.gl/xEaPdr
1.5 – Examining quadratic functions on
various sized intervals to determine average
rates of change
Evaluating exponential functions
https://goo.gl/0hFycg
Average rate of change
https://goo.gl/ZQ7f3T
1.6 – Comparing quadratic and exponential
functions to clarify and distinguish between
types of growth in each as well as how that
growth appears in each of their
representations
Function or not a function
https://goo.gl/qq4aJn
Domain and range
https://goo.gl/7DwLwK
1.7 – Incorporating quadratics with the
understandings of linear and exponential
functions
Transformations of functions
https://goo.gl/qbGsE6
Multiple representations for linear, exponential
and quadratic functions
https://goo.gl/MCzcRl