Desenvolvimento analítico da função quadrática e aplicação - ALMADA, Nilson Gonçalves de (2022)
This article aims to develop a study of the quadratic function considering two different approaches. In the first one, the analytical formalism of the quadratic function is highlighted, considering the main elements that characterize it both from an analytical and geometric point of view. After this approach, the study is applied from applications that contextualize the teaching of the polynomial function of the 2nd degree. In the second approach, a second analytical formalism is developed with demonstrations that show the emergence of a quantity A as a function between the maximum height corresponding to the ordinate point of the vertex with the difference between the abscissas of the vertex with the variable x. In any case, from these results, it becomes possible to establish a relationship between the quantity A, the abscissa of the vertex, with the roots of the quadratic function. This alternative formalism is applied to three problems that can be encountered in everyday situations. The research concludes considering that with the analytical/geometric formalisms developed in view of the applications presented in both, that the study of the quadratic function can receive a new scientific "look", considering that the theory is not restricted only to techniques separated from the context of everyday life, the latter being fundamentally necessary to bring theory to practice, which is essential for an effective teaching and learning process.