{"id":183658,"date":"2024-06-07T16:18:51","date_gmt":"2024-06-07T19:18:51","guid":{"rendered":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/?post_type=eaja&#038;p=183658"},"modified":"2024-06-25T16:33:00","modified_gmt":"2024-06-25T19:33:00","slug":"matematica-identificando-as-equacoes-do-2o-grau","status":"publish","type":"eaja","link":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/eaja\/matematica-identificando-as-equacoes-do-2o-grau\/","title":{"rendered":"Matem\u00e1tica &#8211; Identificando as equa\u00e7\u00f5es do 2\u00ba grau"},"content":{"rendered":"\n<p class=\"has-text-align-center has-medium-font-size\"><strong>Esta proposta de atividade de&nbsp;MATEM\u00c1TICA&nbsp;\u00e9 destinada aos estudante do 6\u00ba Per\u00edodo&nbsp;da Educa\u00e7\u00e3o de Jovens e Adultos\u2013EJA<\/strong><\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=153d2jgjQhYkxN4kTFD-JMr7-H75T1mgt\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE A ATIVIDADE<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1gxHv__PkmAXmCeHx2KDHZCjEddKpAQOt\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE OS SLIDES<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1htSiqNs0zhS91k1hCycLc4cSrNcSPsxD\">BAIXE O TEXTO<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:18% auto\"><figure class=\"wp-block-media-text__media\"><img decoding=\"async\" width=\"205\" height=\"141\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2024\/06\/equacao.png\" alt=\"\" class=\"wp-image-183659 size-full\"\/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-7789f30434f9ba18f1f1d2631d35632e\" style=\"color:#207822\"><strong>Introdu\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Neste texto iremos explorar as <strong>equa\u00e7\u00f5es do 2\u00b0 grau<\/strong>, mais especificamente, na defini\u00e7\u00e3o, nos diferentes tipos, na identifica\u00e7\u00e3o de seus coeficientes e alguns exemplos ilustrativos para melhor compreens\u00e3o.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Imagem:canva.com\/equa\u00e7\u00e3o_<a href=\"https:\/\/l1nk.dev\/Korot\">https:\/\/l1nk.dev\/Korot<\/a><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-32b610643aeda58098691f4b6c91ce61\" style=\"color:#207822\"><strong>Defini\u00e7\u00e3o de Equa\u00e7\u00f5es do 2\u00ba Grau<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Uma equa\u00e7\u00e3o do 2\u00ba grau, ou <strong>equa\u00e7\u00e3o quadr\u00e1tica<\/strong>, \u00e9 uma equa\u00e7\u00e3o polinomial de <strong>grau dois<\/strong>. Sua forma geral \u00e9 dada por:&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-link-color has-medium-font-size wp-elements-8bbcf629e40fe2ec5a6fbe5d3d807556\"><strong>ax<\/strong><strong><sup>2<\/sup><\/strong><strong> + bx + c = 0<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Onde:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">&nbsp;a, b e c s\u00e3o denominados de coeficientes reais com&nbsp; a\u22600.<\/li>\n\n\n\n<li class=\"has-medium-font-size\">ax<sup>2<\/sup>&nbsp; \u00e9 o termo quadr\u00e1tico,&nbsp;<\/li>\n\n\n\n<li class=\"has-medium-font-size\">bx \u00e9 o termo linear e&nbsp;<\/li>\n\n\n\n<li class=\"has-medium-font-size\">c \u00e9 o termo constante.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-c32dc4915ea1b52ebda6d3630384c6d9\" style=\"color:#207822\"><strong>Coeficientes<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Os coeficientes<strong> a<\/strong>, <strong>b<\/strong> e <strong>c<\/strong> s\u00e3o os n\u00fameros que multiplicam os termos da equa\u00e7\u00e3o do 2\u00ba grau:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>a:<\/strong> coeficiente do termo quadr\u00e1tico (n\u00e3o pode ser zero).<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>b:<\/strong> coeficiente do termo linear.<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>c:<\/strong> termo constante.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-649c2099f0a56a781d6d526f602aaa05\" style=\"color:#207822\"><strong>Tipos de Equa\u00e7\u00f5es do 2\u00ba Grau<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">As equa\u00e7\u00f5es do 2\u00ba grau podem ser classificadas em tr\u00eas tipos principais:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>Equa\u00e7\u00e3o Completa:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Cont\u00e9m todos os termos ax<sup>2<\/sup> +bx + c = 0.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>Equa\u00e7\u00e3o Incompleta do Tipo 1:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Falta o termo linear bx, ficando na forma ax<sup>2<\/sup> + c = 0&nbsp;<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>Equa\u00e7\u00e3o Incompleta do Tipo 2:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Falta o termo constante c, ficando na forma ax<sup>2<\/sup> +bx = 0&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-50931dab9f682eacbbd21c295be8cb9c\" style=\"color:#207822\"><strong>Exemplos Simples<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>Equa\u00e7\u00e3o Completa:<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\">2x<sup>2<\/sup> + 3x &#8211; 5 = 0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Aqui, a=2, b=3 e c=\u22125.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>Equa\u00e7\u00e3o Incompleta do Tipo 1:&nbsp;<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\">x<sup>2<\/sup> &#8211; 16 = 0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Neste caso, a = 1, b = 0 e c = &#8211; 16.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>Equa\u00e7\u00e3o Incompleta do Tipo 2:&nbsp;<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\">&#8211; 2x<sup>2<\/sup> &#8211; 7x = 0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Aqui, a = &#8211; 2, b = &#8211; 7 e c = 0.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-fe18f54d6eae9dbbd7c0872024a3a110\" style=\"color:#207822\"><strong>Exemplos Contextualizados<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Trajet\u00f3ria de um Proj\u00e9til<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Ao lan\u00e7ar um proj\u00e9til verticalmente a uma altura h em metros, ap\u00f3s t segundos, sua trajet\u00f3ria pode ser representada pela express\u00e3o<\/p>\n\n\n\n<p class=\"has-medium-font-size\">h(t)=\u22124,9t<sup>2<\/sup> + 14,7t + 20<\/p>\n\n\n\n<p class=\"has-medium-font-size\">A equa\u00e7\u00e3o do 2\u00ba grau utilizada para determinar o tempo gasto para que o projeto retornar ao solo, h = 0, \u00e9&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u22124,9t<sup>2<\/sup> + 14,7t + 20 = 0<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Onde:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">a = \u22124,9, b = 14,7 e c = 20.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\"><strong>\u00c1rea de um Jardim:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Um jardineiro deseja plantar um jardim retangular com \u00e1rea de 60 m\u00b2. A largura \u00e9 x metros e o comprimento \u00e9 (x+4) metros. A equa\u00e7\u00e3o que representa esta situa\u00e7\u00e3o \u00e9:&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">x.(x+3) = 60, resolvendo os par\u00eanteses e igualando a zero, teremos:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">x<sup>2<\/sup> + 3x &#8211; 60 = 0<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Aqui, a = 1, b = 3 e c = -60.<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Ficamos por aqui, at\u00e9 o pr\u00f3ximo.<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Atividades<\/strong><\/p>\n\n\n\n<p class=\"has-light-green-cyan-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 01<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Exemplo de equa\u00e7\u00e3o do 2\u00ba grau do tipo ax<sup>2<\/sup> + c = 0 \u00e9<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(A) x<sup>2<\/sup> &#8211; 9 = 0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(B) x<sup>2<\/sup> + 3x &#8211; 7 = 0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(C) 4x<sup>2<\/sup> + 2x = 0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(D) 7x + 2 = 0.<\/p>\n\n\n\n<p class=\"has-light-green-cyan-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 02<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Um jardineiro est\u00e1 planejando cercar um jardim retangular e quer que a \u00e1rea seja de 120 m\u00b2. Se a largura do jardim for x metros e o comprimento for (x+6) metros, podemos afirmar que a equa\u00e7\u00e3o do 2\u00ba grau que representa esta situa\u00e7\u00e3o \u00e9<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(A) x<sup>2<\/sup> + 6x &#8211; 120 = 0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(B) x<sup>2<\/sup> + 6x + 120 = 0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(C) x<sup>2<\/sup> &#8211; 6x &#8211; 120 = 0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(D) x<sup>2<\/sup> &#8211; 6x + 120 = 0.<\/p>\n\n\n\n<p class=\"has-light-green-cyan-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 03<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Um agricultor planeja criar uma horta em formato retangular cuja \u00e1rea total deve ser de 200 m\u00b2. A largura do jardim \u00e9 x metros e o comprimento \u00e9 (x+12) metros. Formule a equa\u00e7\u00e3o do 2\u00ba grau que representa essa situa\u00e7\u00e3o e indique os valores dos coeficientes a, b e c na equa\u00e7\u00e3o resultante.<\/p>\n\n\n\n<p class=\"has-light-green-cyan-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 04<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Um f\u00edsico est\u00e1 estudando o movimento de um proj\u00e9til lan\u00e7ado verticalmente. A altura h do proj\u00e9til em metros, em fun\u00e7\u00e3o do tempo t em segundos, \u00e9 descrita pela equa\u00e7\u00e3o h(t)=\u22122,7t<sup>2<\/sup> +11,5t+30. Escreva a equa\u00e7\u00e3o do 2\u00ba grau relacionada a essa situa\u00e7\u00e3o e identifique os coeficientes a, b e c. Descreva como voc\u00ea identificou cada um dos coeficientes.<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>Autoria<\/td><td>Professor H\u00e9lio Roberto da Rocha, Mestre em matem\u00e1tica<\/td><\/tr><tr><td>Componente curricular<\/td><td>Matem\u00e1tica<\/td><\/tr><tr><td>Objetivos de aprendizagem e desenvolvimento<\/td><td>(EJAMA0610) Reconhecer uma equa\u00e7\u00e3o do 2\u00ba grau, identificando seus coeficientes na forma completa e nas formas incompletas quando apresentada em situa\u00e7\u00f5es-problema, bem como determinar as ra\u00edzes por meio da fatora\u00e7\u00e3o o f\u00f3rmula de resolutiva.<\/td><\/tr><tr><td>Refer\u00eancias<\/td><td>SOUZA, Joamir Roberto de: Matem\u00e1tica realidade &amp; tecnologia: 6\u00ba ao 9\u00ba ano: ensino fundamental: anos finais \/Joamir Roberto de Souza. \u2013 1. ed. \u2013 S\u00e3o Paulo: FTD, 2018.<br>GIOVANNI J\u00daNIOR, Jos\u00e9 Ruy &#8211; A conquista da matem\u00e1tica: 6\u00ba ao 9\u00b0 ano: ensino fundamental: anos finais \/ Jos\u00e9 Ruy Giovanni J\u00fanior, Benedicto Castrucci. \u2014 4. ed. \u2014 S\u00e3o Paulo: FTD, 2018.<br>GOI\u00c2NIA. Secretaria Municipal de Educa\u00e7\u00e3o. Aprender Sempre. 6\u00ba ao 9\u00ba ano &#8211; Ensino Fundamental; Matem\u00e1tica; Goi\u00e2nia, 2024.<br><\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"author":47,"featured_media":183661,"template":"","meta":{"_acf_changed":false,"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":""},"eaja_categoria":[69],"serie":[100],"eaja_componente":[78],"class_list":["post-183658","eaja","type-eaja","status-publish","has-post-thumbnail","hentry","eaja_categoria-2o-segmento-7a-e-8a-serie","serie-8a-serie","eaja_componente-matematica","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja\/183658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja"}],"about":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/types\/eaja"}],"author":[{"embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/users\/47"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media\/183661"}],"wp:attachment":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media?parent=183658"}],"wp:term":[{"taxonomy":"eaja_categoria","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_categoria?post=183658"},{"taxonomy":"serie","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/serie?post=183658"},{"taxonomy":"eaja_componente","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_componente?post=183658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}