A importância do método de completar quadrados e suas aplicações em Geometria Analítica

This work aimed to understand the need to understand the method of completing squares, a fundamental technique for solving quadratic equations and analyzing geometric places, through its applications in Analytical Geometry studies. Because, often, this technique’s power of application is underestima...

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Detalles Bibliográficos
Autor: BATISTA, Ezequiel Gomes
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2024
País:Brasil
Institución:Universidade Federal do Maranhão (UFMA)
Repositorio:Biblioteca Digital de Teses e Dissertações da UFMA
Idioma:portugués
OAI Identifier:oai:tede2:tede/5661
Acceso en línea:https://tedebc.ufma.br/jspui/handle/tede/5661
Access Level:acceso abierto
Palabra clave:equação do segundo grau;
cônicas;
método de completar quadrados;
quadratic equation;
conics;
method of completing squares.
Matemática
Descripción
Sumario:This work aimed to understand the need to understand the method of completing squares, a fundamental technique for solving quadratic equations and analyzing geometric places, through its applications in Analytical Geometry studies. Because, often, this technique’s power of application is underestimated and its teaching is neglected or presented only in a punctual manner. To this end, a bibliographical search was carried out on the topic through several books on the history of mathematics, books on Analytical Geometry and recent articles on the subject. It was then seen that this tool cannot be associated only with the study of quadratic equations in elementary school. To justify this, the method was explored in some contexts of Analytical Geometry, especially in the association between the general quadratic equation with two unknowns and the equations that represent classical curves (circumference and other conics) when compared with the extended version of these equations.