Funções quadráticas, contextualização, análise gráfica e aplicações
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/4462 |
Resumo: | 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. |
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Souza, Mário José dehttp://lattes.cnpq.br/4862963990848505Souza, Mário José deVasconcelos, José Éder SalvadorDias, Ivonildes Ribeiro Martinshttp://lattes.cnpq.br/0287387104567521Menezes, Ruimar Calaça de2015-04-27T13:14:20Z2015-03-06MENEZES, R. C. Funções quadráticas, contextualização, análise gráfica e aplicações. 2014. 70 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional ) - Universidade Federal de Goiás, Goiânia, 2015.http://repositorio.bc.ufg.br/tede/handle/tede/4462The 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.Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-04-27T13:09:17Z No. of bitstreams: 2 Dissertação - Ruimar Calaça de Menezes - 2014.pdf: 3563938 bytes, checksum: 780f3827908c962633ef10e7001a936e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-04-27T13:14:20Z (GMT) No. of bitstreams: 2 Dissertação - Ruimar Calaça de Menezes - 2014.pdf: 3563938 bytes, checksum: 780f3827908c962633ef10e7001a936e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2015-04-27T13:14:20Z (GMT). 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dc.title.por.fl_str_mv |
Funções quadráticas, contextualização, análise gráfica e aplicações |
title |
Funções quadráticas, contextualização, análise gráfica e aplicações |
spellingShingle |
Funções quadráticas, contextualização, análise gráfica e aplicações Menezes, Ruimar Calaça de Função quadrática Parábola Seções cônicas Geogebra Quadratic function Parable Conic sections Geogebra CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Funções quadráticas, contextualização, análise gráfica e aplicações |
title_full |
Funções quadráticas, contextualização, análise gráfica e aplicações |
title_fullStr |
Funções quadráticas, contextualização, análise gráfica e aplicações |
title_full_unstemmed |
Funções quadráticas, contextualização, análise gráfica e aplicações |
title_sort |
Funções quadráticas, contextualização, análise gráfica e aplicações |
author |
Menezes, Ruimar Calaça de |
author_facet |
Menezes, Ruimar Calaça de |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Souza, Mário José de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/4862963990848505 |
dc.contributor.referee1.fl_str_mv |
Souza, Mário José de |
dc.contributor.referee2.fl_str_mv |
Vasconcelos, José Éder Salvador |
dc.contributor.referee3.fl_str_mv |
Dias, Ivonildes Ribeiro Martins |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/0287387104567521 |
dc.contributor.author.fl_str_mv |
Menezes, Ruimar Calaça de |
contributor_str_mv |
Souza, Mário José de Souza, Mário José de Vasconcelos, José Éder Salvador Dias, Ivonildes Ribeiro Martins |
dc.subject.por.fl_str_mv |
Função quadrática Parábola Seções cônicas Geogebra |
topic |
Função quadrática Parábola Seções cônicas Geogebra Quadratic function Parable Conic sections Geogebra CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Quadratic function Parable Conic sections Geogebra |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
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. |
publishDate |
2015 |
dc.date.accessioned.fl_str_mv |
2015-04-27T13:14:20Z |
dc.date.issued.fl_str_mv |
2015-03-06 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
MENEZES, R. C. Funções quadráticas, contextualização, análise gráfica e aplicações. 2014. 70 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional ) - Universidade Federal de Goiás, Goiânia, 2015. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/4462 |
identifier_str_mv |
MENEZES, R. C. Funções quadráticas, contextualização, análise gráfica e aplicações. 2014. 70 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional ) - Universidade Federal de Goiás, Goiânia, 2015. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/4462 |
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por |
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por |
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600 600 600 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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UFG |
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Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Matemática e Estatística - IME (RG) |
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Universidade Federal de Goiás |
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