Quadratic functions and equations. Surfaces under scrutiny

Abstract

The present work presents the didactic and mathematical foundations related to the concepts of quadratic functions and equations within the implemented teaching proposal for a 4th-year course in Secondary Education. The article encompasses both the mathematical underpinning of these concepts and a didactic analysis regarding perspectives, challenges, and requirements linked to teaching quadratic equations and functions. Itexamines the importance and limitations of approaching these areas from both an algebraic and graphical standpoint, highlighting that the application of geometric problematic situations provides a greater sense to the abstract aspects of algebra. For a comprehensive analysis of the teaching proposal, examples derived from practical classroom experience are provided.