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Computationally Supported Study of Quadratic Functions Depending on Parameters

  • Sergei AbramovichEmail author
Chapter
  • 1.1k Downloads
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 3)

Abstract

This chapter further emphasizes the importance of mathematical knowledge by teachers of secondary mathematics in the context of TEMP. Using quadratic functions as background, the chapter introduces the notion of necessary and sufficient conditions, the use of the concept of locus of an algebraic equation with a single parameter, the use of phase diagrams in the case of equations and functions depending on two parameters, the use of qualitative methods in exploring the behavior of solutions to quadratic equations with parameters. It further emphasizes the importance of seeing problem solving as a springboard into the domain of problem posing, demonstrates combinatorial connections, and investigates the behavior of solutions of two quadratic equations depending on the same as well as different parameters.

Keywords

Quadratic function Parameter Discriminant Viéte’s theorem Locus Extreme values Necessary conditions Sufficient conditions Problem posing Qualitative methods Location of roots Permutation Partitioning diagrams the Graphing Calculator Maple Wolfram Alpha 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.State University of New York at PotsdamPotsdamUSA

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