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Gr. HS Unit: Quadratic Functions and Modeling

Unit Overview

In this unit, students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students explore the effects of transformations on quadratic functions in preparation for their work in Geometry. Students expand their experience with functions to include more specialized functions–absolute value, square root, cube root, step, and those that are piecewise-defined. They select the best fitting function to model phenomena.

Essential Questions:

  • When and how is mathematical modeling used to solve real world problems?
    • How are functions used to solve real world problems?
    • Which function is the best fit for the situation?
  • What characteristics of problems would determine how to model the situation and develop a problem solving strategy?
    • What characteristics of problems would help to distinguish whether the situation could be modeled by a particular type of function?
    • When is it advantageous to represent relationships between quantities symbolically? numerically? graphically?
  • Why is it necessary to follow set rules/procedures/properties when manipulating numeric or algebraic expressions?
    • How can the algebraic representation of a function be rearranged to make it easier to indentify attributes of the graph of the function?

A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourges re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.

Unit Lesson

Additional information such as Teachers Notes, Enduring Understandings,Content Emphasis by Cluster, Focus Standards, Possible Student Outcomes, Essential Skills and Knowledge Statements and Clarifications, and Interdisciplinary Connections can be found in this Lesson Unit.