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Previous issue date: 2015-03-06 / The objective of this study is to present the Quadratic Function in a new graphic
perspective. The Quadratic Function content is taught in the ninth year of elementary
school and rst year of high school, the following concepts are learned: equations and
inequalities involving polynomials of second degree, graphing, concavity, zeros of the
quadratic function, the parable vertex, minimum or maximum and applications in other
elds of knowledge.
Two mathematical softwares, Winplot and Geogebra, were used in order to facilitate
the understanding of graphic representations of functions. The parable was discussed
from a historical point of view that also included the concept of speci c terms and
de nitions involving functions. The concept of tangent lines to growth and decrease
of functions was related. The parable was also exhibited in the context of Analytic
Geometry and Calculus, emphasizing the in
uence of each coe cient in relation to the
graph. The parable was studied as one of the conic sections so studied by Apollonius.
Some applications of the parable in daily life, physics and modeling problems were
cited. / Este trabalho tem como objetivo apresentar a Fun c~ao quadr atica em uma nova
perspectiva gr a ca. O conte udo Fun c~ao Quadr atica e ensinado no nono ano do Ensino
Fundamental e primeira s erie do Ensino M edio, sendo trabalhados os seguintes conceitos:
equa c~oes e inequa c~oes envolvendo polin^omios de 2o grau, representa c~ao gr a ca,
concavidade, zeros da fun c~ao quadr atica, v ertice da par abola, valor m nimo ou m aximo
e aplica c~oes em outras areas do conhecimento.
Para desenvolver este trabalho, foram utilizados os softwares matem aticos Winplot
e Geogebra, com o intuito de facilitar a compreens~ao das representa c~oes gr a cas
das fun c~oes. A par abola foi comentada a partir de um contexto hist orico e abrangeu
tamb em o conceito de termos espec cos e de ni c~oes envolvendo fun c~oes. Foi relacionado
o conceito de retas tangentes ao crescimento e decrescimento das fun c~oes.
Tamb em foi exibido a par abola no contexto da Geometria Anal tica e do c alculo diferencial,
salientando a in
u^encia de cada coe ciente em rela c~ao ao gr a co. A par abola
foi estudada como uma das sec c~oes c^onicas t~ao pesquisadas por Apol^onio. Foi citada
algumas aplica c~oes da par abola no cotidiano, na f sica e em problemas de modelagem.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.bc.ufg.br:tede/4462 |
| Date | 06 March 2015 |
| Creators | Menezes, Ruimar Calaça de |
| Contributors | Souza, Mário José de, Souza, Mário José de, Vasconcelos, José Éder Salvador, Dias, Ivonildes Ribeiro Martins |
| Publisher | Universidade Federal de Goiás, Programa de Pós-graduação em PROFMAT (RG), UFG, Brasil, Instituto de Matemática e Estatística - IME (RG) |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFG, instname:Universidade Federal de Goiás, instacron:UFG |
| Rights | http://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess |
| Relation | 5637905143957969341, 600, 600, 600, -4268777512335152015, -7090823417984401694 |
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