Funções quadráticas na sala de aula: uma proposta de ensino através da modelagem matemática

Abstract

We propose a didactic approach to teaching quadratic functions through mathematical modeling. The proposal is based on a problem that requires determining one side of a rectangle as a function of the height of a trapezoid formed within a triangle, under the condition that the areas of the regions formed are equal. Additionally, the triangle and the rectangle must have the same total areas and heights. We explored this problem situation through an experiment involving the transfer of liquids by gravity between triangular and rectangular reservoirs, allowing students to manipulate, investigate, and validate mathematical concepts. The use of tools such as spreadsheets and GeoGebra simulations provided a dynamic learning environment, enhancing the understanding of the properties of quadratic functions. The proposal was implemented with a first-year high school class, followed by an analysis of the results obtained.