{"id":3067,"date":"2025-12-05T11:29:23","date_gmt":"2025-12-05T14:29:23","guid":{"rendered":"https:\/\/hotpixel.me\/geogebra\/?p=3067"},"modified":"2025-12-05T11:30:01","modified_gmt":"2025-12-05T14:30:01","slug":"funcoes-em-movimento-como-os-coeficientes-transformam-graficos-de-1o-e-2o-graus","status":"publish","type":"post","link":"https:\/\/hotpixel.me\/geogebra\/funcoes-em-movimento-como-os-coeficientes-transformam-graficos-de-1o-e-2o-graus\/","title":{"rendered":"Fun\u00e7\u00f5es em movimento: como os coeficientes transformam gr\u00e1ficos de 1\u00ba e 2\u00ba graus"},"content":{"rendered":"<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\" data-spm-anchor-id=\"a2ty_o01.29997173.0.i102.266551713suZjG\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Objetivos de Aprendizagem<\/span><\/strong><\/p>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Analisar os efeitos dos coeficientes nas fun\u00e7\u00f5es afim (<span class=\"qwen-markdown-latex\" translate=\"no\"><span class=\"katex\"><span class=\"katex-mathml\">y=ax+b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span>) e quadr\u00e1tica (<span class=\"qwen-markdown-latex\" translate=\"no\"><span class=\"katex\"><span class=\"katex-mathml\">y=ax2+bx+c<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>).<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Relacionar mudan\u00e7as nos par\u00e2metros com transforma\u00e7\u00f5es no gr\u00e1fico (inclina\u00e7\u00e3o, deslocamento, abertura, concavidade).<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Desenvolver a capacidade de prever o comportamento de uma fun\u00e7\u00e3o a partir de sua lei alg\u00e9brica.<\/span><\/li>\n<\/ul>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Tempo Estimado<\/span><\/strong><\/p>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">2 aulas de 50 minutos<\/span><\/p>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Recursos Necess\u00e1rios<\/span><\/strong><\/p>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Dispositivos com acesso ao GeoGebra<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Projetor<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Caderno de investiga\u00e7\u00f5es ou ficha \u201cLaborat\u00f3rio de Fun\u00e7\u00f5es\u201d<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Sliders (controles deslizantes) pr\u00e9-configurados (opcional \u2014 voc\u00ea pode criar na hora com os alunos)<\/span><\/li>\n<\/ul>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Passo a Passo<\/span><\/strong><\/p>\n<p class=\"qwen-markdown-paragraph\"><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Aula 1 \u2013 Fun\u00e7\u00e3o Afim (<\/span><span class=\"qwen-markdown-latex\" translate=\"no\"><span class=\"katex\"><span class=\"katex-mathml\">y=ax+b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span><span class=\"qwen-markdown-text\">)<\/span><\/strong><\/p>\n<ol class=\"qwen-markdown-list\" dir=\"auto\" start=\"1\">\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Pergunta disparadora (5 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\"><em>\u201cSe eu mudar s\u00f3 o n\u00famero da frente do x, o que acontece com a reta? E se eu mudar s\u00f3 o n\u00famero sem x?\u201d<\/em><\/span><\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Constru\u00e7\u00e3o interativa (30 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">No GeoGebra, crie dois <strong class=\"qwen-markdown-strong\">sliders<\/strong>:<\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\"><code class=\"qwen-markdown-codespan\">a<\/code> (de -5 a 5)<\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><code class=\"qwen-markdown-codespan\">b<\/code> (de -5 a 5)<\/span><\/li>\n<\/ul>\n<div class=\"qwen-markdown-space\"><\/div>\n<\/li>\n<li><span class=\"qwen-markdown-text\">Digite na barra de entrada: <code class=\"qwen-markdown-codespan\">y = a*x + b<\/code><\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Pe\u00e7a que os alunos:<br \/>\na) Observem o gr\u00e1fico enquanto movem <code class=\"qwen-markdown-codespan\">a<\/code> (fixando <code class=\"qwen-markdown-codespan\">b = 0<\/code>).<br \/>\nb) Depois, movam <code class=\"qwen-markdown-codespan\">b<\/code> (fixando <code class=\"qwen-markdown-codespan\">a = 1<\/code>).<br \/>\nc) Anotem:<\/span><\/p>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">O que acontece com a inclina\u00e7\u00e3o?<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">O que acontece com o ponto onde a reta corta o eixo Y?<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Desafios r\u00e1pidos (15 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\"><em>\u201cFa\u00e7a uma reta que suba devagar.\u201d<\/em><\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><em>\u201cCrie uma reta horizontal.\u201d<\/em><\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><em>\u201cMostre uma reta que cruze o eixo Y em (0, -3).\u201d<\/em><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p class=\"qwen-markdown-paragraph\"><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Aula 2 \u2013 Fun\u00e7\u00e3o Quadr\u00e1tica (<\/span><span class=\"qwen-markdown-latex\" translate=\"no\"><span class=\"katex\"><span class=\"katex-mathml\">y=ax2+bx+c<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span><span class=\"qwen-markdown-text\">)<\/span><\/strong><\/p>\n<ol class=\"qwen-markdown-list\" dir=\"auto\" start=\"1\">\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Transi\u00e7\u00e3o (5 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\"><em>\u201cE se em vez de reta, tivermos uma curva? O que controla o \u2018formato\u2019 do U?\u201d<\/em><\/span><\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Constru\u00e7\u00e3o com tr\u00eas sliders (30 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Crie sliders para <code class=\"qwen-markdown-codespan\">a<\/code>, <code class=\"qwen-markdown-codespan\">b<\/code> e <code class=\"qwen-markdown-codespan\">c<\/code> (ex: de -4 a 4).<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Digite: <code class=\"qwen-markdown-codespan\">y = a*x^2 + b*x + c<\/code><\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Explore em etapas:<br \/>\na) Fixe <code class=\"qwen-markdown-codespan\">b = 0<\/code>, <code class=\"qwen-markdown-codespan\">c = 0<\/code> \u2192 varie <code class=\"qwen-markdown-codespan\">a<\/code>: abertura e concavidade.<br \/>\nb) Fixe <code class=\"qwen-markdown-codespan\">a = 1<\/code>, <code class=\"qwen-markdown-codespan\">b = 0<\/code> \u2192 varie <code class=\"qwen-markdown-codespan\">c<\/code>: deslocamento vertical.<br \/>\nc) Fixe <code class=\"qwen-markdown-codespan\">a = 1<\/code>, <code class=\"qwen-markdown-codespan\">c = 0<\/code> \u2192 varie <code class=\"qwen-markdown-codespan\">b<\/code>: movimento lateral e do v\u00e9rtice.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Investiga\u00e7\u00e3o guiada (15 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Preencham a ficha respondendo:<\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\"><em>\u201cO que faz a par\u00e1bola abrir mais ou fechar?\u201d<\/em><\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><em>\u201cComo sabemos se ela tem \u2018boca pra cima\u2019 ou \u2018pra baixo\u2019?\u201d<\/em><\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><em>\u201cOnde fica o v\u00e9rtice quando mudamos <code class=\"qwen-markdown-codespan\">b<\/code>?\u201d<\/em><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Dicas para Maximizar a Aprendizagem<\/span><\/strong><\/p>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Use <strong class=\"qwen-markdown-strong\">cores diferentes<\/strong> para cada tipo de fun\u00e7\u00e3o (azul para afim, vermelho para quadr\u00e1tica).<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Evite dar regras prontas \u2014 deixe que os alunos <strong class=\"qwen-markdown-strong\">formulem as conclus\u00f5es<\/strong> com base nas observa\u00e7\u00f5es.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Relacione com fen\u00f4menos reais:<\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Fun\u00e7\u00e3o afim \u2192 custo total com valor fixo + vari\u00e1vel<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Fun\u00e7\u00e3o quadr\u00e1tica \u2192 trajet\u00f3ria de um lan\u00e7amento<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<blockquote class=\"qwen-markdown-blockquote\">\n<p class=\"qwen-markdown-paragraph\"><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Material Complementar Sugerido:<\/span><\/strong><br \/>\n<strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">\u201cLaborat\u00f3rio de Fun\u00e7\u00f5es\u201d<\/span><\/strong><span class=\"qwen-markdown-text\"> \u2013 ficha com tabelas, espa\u00e7os para esbo\u00e7os e perguntas investigativas. Dispon\u00edvel para download.<\/span><\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd39 Objetivos de Aprendizagem Analisar os efeitos dos coeficientes nas fun\u00e7\u00f5es afim (y=ax+by=ax+b) e quadr\u00e1tica (y=ax2+bx+cy=ax2+bx+c). Relacionar mudan\u00e7as nos par\u00e2metros com transforma\u00e7\u00f5es no gr\u00e1fico (inclina\u00e7\u00e3o, deslocamento, abertura, concavidade). Desenvolver a capacidade de prever o comportamento de uma fun\u00e7\u00e3o a partir de sua lei alg\u00e9brica. \ud83d\udd39 Tempo Estimado 2 aulas de 50 minutos \ud83d\udd39 Recursos Necess\u00e1rios [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[34],"tags":[],"class_list":["post-3067","post","type-post","status-publish","format-standard","hentry","category-9o-ano"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts\/3067","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/comments?post=3067"}],"version-history":[{"count":1,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts\/3067\/revisions"}],"predecessor-version":[{"id":3068,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts\/3067\/revisions\/3068"}],"wp:attachment":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/media?parent=3067"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/categories?post=3067"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/tags?post=3067"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}