{"id":1043,"date":"2024-04-27T21:00:57","date_gmt":"2024-04-28T00:00:57","guid":{"rendered":"https:\/\/matematicasaomiguel.com.br\/?page_id=1043"},"modified":"2025-09-01T12:28:32","modified_gmt":"2025-09-01T15:28:32","slug":"torre-de-hanoi","status":"publish","type":"page","link":"https:\/\/matematicasaomiguel.com.br\/?page_id=1043","title":{"rendered":"Equa\u00e7\u00f5es"},"content":{"rendered":"\t\t
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\n\t\t\t\t\t\r\n\r\n\r\n \r\n \r\n Resolu\u00e7\u00e3o de Equa\u00e7\u00f5es<\/title>\r\n <script src=\"https:\/\/cdn.plot.ly\/plotly-latest.min.js\"><\/script>\r\n<\/head>\r\n<body>\r\n <h2>Resolu\u00e7\u00e3o de Equa\u00e7\u00f5es<\/h2>\r\n\r\n <h3>Equa\u00e7\u00e3o do Primeiro Grau: ax + b = 0<\/h3>\r\n <label for=\"a1\">a: <\/label>\r\n <input type=\"number\" id=\"a1\"><br>\r\n <label for=\"b1\">b: <\/label>\r\n <input type=\"number\" id=\"b1\"><br>\r\n <button onclick=\"resolverPrimeiroGrau()\">Resolver Primeiro Grau<\/button>\r\n <div id=\"resultado1\"><\/div>\r\n <hr>\r\n\r\n <h3>Equa\u00e7\u00e3o do Segundo Grau: ax\u00b2 + bx + c = 0<\/h3>\r\n <label for=\"a2\">a: <\/label>\r\n <input type=\"number\" id=\"a2\"><br>\r\n <label for=\"b2\">b: <\/label>\r\n <input type=\"number\" id=\"b2\"><br>\r\n <label for=\"c2\">c: <\/label>\r\n <input type=\"number\" id=\"c2\"><br>\r\n <button onclick=\"resolverSegundoGrau()\">Resolver Segundo Grau<\/button>\r\n <div id=\"resultado2\"><\/div>\r\n <hr>\r\n\r\n <h3>Gr\u00e1fico da Fun\u00e7\u00e3o Quadr\u00e1tica<\/h3>\r\n <label for=\"intervaloInicio\">In\u00edcio do intervalo em x: <\/label>\r\n <input type=\"number\" id=\"intervaloInicio\" value=\"-10\"><br>\r\n <label for=\"intervaloFim\">Fim do intervalo em x: <\/label>\r\n <input type=\"number\" id=\"intervaloFim\" value=\"10\"><br>\r\n \r\n <label for=\"yInicio\">In\u00edcio do intervalo em y: <\/label>\r\n <input type=\"number\" id=\"yInicio\" value=\"-10\"><br>\r\n <label for=\"yFim\">Fim do intervalo em y: <\/label>\r\n <input type=\"number\" id=\"yFim\" value=\"10\"><br>\r\n \r\n <button onclick=\"plotarGrafico()\">Plotar Gr\u00e1fico<\/button>\r\n <div id=\"grafico\"><\/div>\r\n\r\n <script>\r\n function resolverPrimeiroGrau() {\r\n var a = parseFloat(document.getElementById(\"a1\").value);\r\n var b = parseFloat(document.getElementById(\"b1\").value);\r\n var resultado = document.getElementById(\"resultado1\");\r\n if (a == 0) {\r\n resultado.innerHTML = \"N\u00e3o \u00e9 uma equa\u00e7\u00e3o do primeiro grau.\";\r\n } else {\r\n var solucao = -b \/ a;\r\n resultado.innerHTML = \"Solu\u00e7\u00e3o: x = \" + solucao.toFixed(2);\r\n }\r\n }\r\n\r\n function resolverSegundoGrau() {\r\n var a = parseFloat(document.getElementById(\"a2\").value);\r\n var b = parseFloat(document.getElementById(\"b2\").value);\r\n var c = parseFloat(document.getElementById(\"c2\").value);\r\n var resultado = document.getElementById(\"resultado2\");\r\n\r\n if (a === 0) {\r\n resultado.innerHTML = \"N\u00e3o \u00e9 uma equa\u00e7\u00e3o do segundo grau.\";\r\n return;\r\n }\r\n\r\n var delta = b * b - 4 * a * c;\r\n if (delta < 0) {\r\n resultado.innerHTML = \"N\u00e3o existem solu\u00e7\u00f5es reais.\";\r\n } else if (delta == 0) {\r\n var solucao = -b \/ (2 * a);\r\n resultado.innerHTML = \"Solu\u00e7\u00e3o \u00fanica: x = \" + solucao.toFixed(2);\r\n } else {\r\n var solucao1 = (-b + Math.sqrt(delta)) \/ (2 * a);\r\n var solucao2 = (-b - Math.sqrt(delta)) \/ (2 * a);\r\n resultado.innerHTML = \"Solu\u00e7\u00f5es: x1 = \" + solucao1.toFixed(2) + \", x2 = \" + solucao2.toFixed(2);\r\n }\r\n }\r\n\r\n function plotarGrafico() {\r\n var a = parseFloat(document.getElementById(\"a2\").value);\r\n var b = parseFloat(document.getElementById(\"b2\").value);\r\n var c = parseFloat(document.getElementById(\"c2\").value);\r\n var inicio = parseFloat(document.getElementById(\"intervaloInicio\").value);\r\n var fim = parseFloat(document.getElementById(\"intervaloFim\").value);\r\n var yInicio = parseFloat(document.getElementById(\"yInicio\").value);\r\n var yFim = parseFloat(document.getElementById(\"yFim\").value);\r\n\r\n if (a === 0) {\r\n alert(\"Informe um valor de 'a' diferente de zero para o gr\u00e1fico da par\u00e1bola.\");\r\n return;\r\n }\r\n\r\n \/\/ Pontos da fun\u00e7\u00e3o\r\n var x_vals = [];\r\n var y_vals = [];\r\n for (var x = inicio; x <= fim; x += 0.1) {\r\n x_vals.push(x);\r\n y_vals.push(a * x * x + b * x + c);\r\n }\r\n\r\n \/\/ V\u00e9rtice\r\n var xv = -b \/ (2 * a);\r\n var yv = a * xv * xv + b * xv + c;\r\n\r\n \/\/ Ra\u00edzes reais (se existirem)\r\n var delta = b * b - 4 * a * c;\r\n var raizes_x = [];\r\n var raizes_y = [];\r\n if (delta >= 0) {\r\n var x1 = (-b + Math.sqrt(delta)) \/ (2 * a);\r\n var x2 = (-b - Math.sqrt(delta)) \/ (2 * a);\r\n raizes_x = [x1, x2];\r\n raizes_y = [0, 0];\r\n }\r\n\r\n \/\/ Dados do gr\u00e1fico\r\n var data = [\r\n {\r\n x: x_vals,\r\n y: y_vals,\r\n type: 'scatter',\r\n name: 'Par\u00e1bola'\r\n },\r\n {\r\n x: [xv],\r\n y: [yv],\r\n mode: 'markers+text',\r\n text: ['V\u00e9rtice'],\r\n textposition: 'top center',\r\n marker: { size: 10, color: 'red' },\r\n name: 'V\u00e9rtice'\r\n },\r\n {\r\n x: raizes_x,\r\n y: raizes_y,\r\n mode: 'markers+text',\r\n text: raizes_x.map((r, i) => \"x\" + (i + 1)),\r\n textposition: 'bottom center',\r\n marker: { size: 10, color: 'green' },\r\n name: 'Ra\u00edzes'\r\n }\r\n ];\r\n\r\n \/\/ Layout com intervalos definidos\r\n var layout = {\r\n xaxis: {\r\n title: 'x',\r\n range: [inicio, fim],\r\n zeroline: true\r\n },\r\n yaxis: {\r\n title: 'y',\r\n range: [yInicio, yFim],\r\n zeroline: true\r\n },\r\n title: \"Gr\u00e1fico da Fun\u00e7\u00e3o Quadr\u00e1tica\"\r\n };\r\n\r\n Plotly.newPlot('grafico', data, layout);\r\n }\r\n <\/script>\r\n<\/body>\r\n<\/html>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Resolu\u00e7\u00e3o de Equa\u00e7\u00f5es Resolu\u00e7\u00e3o de Equa\u00e7\u00f5es Equa\u00e7\u00e3o do Primeiro Grau: ax + b = 0 a: b: Resolver Primeiro Grau […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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