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Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  1. 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.
  2. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = , y = , y = , y = , and classify them as representing exponential growth or decay.
Standard #: MAFS.912.F-IF.3.8Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Functions: Interpreting Functions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Analyze functions using different representations. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
Formative Assessments
  • Exponential Functions - 2 # Students are asked to identify the percent rate of change of a given exponential function.
  • Exponential Functions - 1 # Students are asked to identify the percent rate of change of a given exponential function.
  • A Home for Fido # Students are asked to rewrite a quadratic function in an equivalent form by completing the square and to use this form to identify the vertex of the graph and explain its meaning in context.
  • Launch From a Hill # Students are asked to factor and find the zeros of a polynomial function given in context.
Lesson Plans
  • The Towers of Hanoi: Experiential Recursive Thinking #
    This lesson is about the Towers of Hanoi problem, a classic famous problem involving recursive thinking to reduce what appears to be a very large and difficult problem into a series of simpler ones.  The learning objective is for students to begin to understand recursive logic and thinking, relevant to computer scientists, mathematicians and engineers.   The lesson is experiential, in that each student will be working with her/his own Towers of Hanoi manipulative, inexpensively obtained.  There is no formal prerequisite, although some familiarity with set theory and functions is helpful.  The last three sections of the lesson involve some more formal concepts with recursive equations and proof by induction, so the students who work on those sections should probably be level 11 or 12 in a K-12 educational system.  The lesson has a Stop Point for 50-minute classes, followed by three more segments that may require a half to full additional class time.  So the teacher may use only those segments up to the Stop Point, or if two class sessions are to be devoted to the lesson, the entire set of segments.  Supplies are modest, and may be a set of coins or some washers from a hardware store to assemble small piles of disks in front of each student, each set of disks representing a Towers of Hanoi manipulative.  Or the students may assemble before the class a more complete Towers of Hanoi at home, as demonstrated in the video.  The classroom activities involve attempting to solve with hand and mind the Towers of Hanoi problem and discussing with fellow students patterns in the process and strategies for solution.
  • Functions and Everyday Situations # This lesson unit is intended to help you assess how well students are able to articulate verbally the relationships between variables arising in everyday contexts, translate between everyday situations and sketch graphs of relationships between variables, interpret algebraic functions in terms of the contexts in which they arise and reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.
  • Forming Quadratics # This lesson unit is intended to help you assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help you identify and help students who have the following difficulties in understanding how the factored form of the function can identify a graph's roots, how the completed square form of the function can identify a graph's maximum or minimum point, and how the standard form of the function can identify a graph's intercept.
  • Exponential Graphing Using Technology # This lesson is teacher/student directed for discovering and translating exponential functions using a graphing app. The lesson focuses on the translations from a parent graph and how changing the coefficient, base and exponent values relate to the transformation.
Original Student Tutorial
Perspectives Video: Expert
Problem-Solving Tasks
  • Which Function? # The task addresses knowledge related to interpreting forms of functions derived by factoring or completing the square. It requires students to pay special attention to the information provided by the way the equation is represented as well as the sign of the leading coefficient, which is not written out explicitly, and then to connect this information to the important features of the graph.
  • Springboard Dive # The problem presents a context where a quadratic function arises. Careful analysis, including graphing of the function, is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.
Tutorial
Unit/Lesson Sequence
  • Sample Algebra 1 Curriculum Plan Using CMAP #
    This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS. Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

    Using this CMAP

    To view an introduction on the CMAP tool, please . To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app. To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx
Video/Audio/Animations
Worksheet
  • Quadratic Functions # This worksheet gives students one place to show all transformations (reflections, vertical stretches/compressions, and translations) for the quadratic function. The worksheet also has a place for domain and range for each transformation.
MFAS Formative Assessments
  • A Home for Fido # Students are asked to rewrite a quadratic function in an equivalent form by completing the square and to use this form to identify the vertex of the graph and explain its meaning in context.
  • Exponential Functions - 1 # Students are asked to identify the percent rate of change of a given exponential function.
  • Exponential Functions - 2 # Students are asked to identify the percent rate of change of a given exponential function.
  • Launch From a Hill # Students are asked to factor and find the zeros of a polynomial function given in context.
Original Student Tutorials Mathematics - Grades 9-12
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