Uma investigação sobre a utilização da função quadrática na representação de situações reais.

Abstract

The quadratic function is a topic in high school curriculum that is frequently explored in textbooks to represent various situations, but it is noticeable that, in general, the mathematical model is already presented, leaving the student simply with the mechanical procedure of determining values  from algebraic expressions, such as the image of the function, the real roots, if they exist, the coordinates of the vertex, and so on. This article aims to contribute to an important question in students' learning on the subject: Given a real-world situation, when can a quadratic function be considered a good model to represent it?    Therefore, this article investigates this question through the analysis of data and contextualized situations. Initially, three situations were analyzed: one idealized, where the model exactly represents the real-situation; one based on experimental data, where, through observation of the data, a quadratic function is identified to represent it, and the extent to which this modeling can adequately represent the situation is investigated; and finally, an example where the quadratic function is not adequate. This type of investigation uses tables, comparisons between values  and algebraic procedures, graphical representations, and some computational resources to build and compare models. Thus, the results allow students to understand that the format of the graph or the possibility of finding a function that approximates the data may not be sufficient to adequately represent reality; rather, the observed context, the analyzed interval, and the objective of the modeling in question must be taken into consideration. In this approach, the student goes beyond simply applying a formula predetermined by a model, but also investigates, tests, and participates in the investigation of its validity, fostering more critical and participatory learning.