{"id":14713,"date":"2018-04-19T22:50:58","date_gmt":"2018-04-19T21:50:58","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14713"},"modified":"2022-01-15T22:22:22","modified_gmt":"2022-01-15T22:22:22","slug":"determina-analiticamente-as-coordenadas-dos-pontos-de-intersecao-dos-graficos-de-f-e-g","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14713","title":{"rendered":"Determina analiticamente as coordenadas dos pontos de interse\u00e7\u00e3o dos gr\u00e1ficos de <em>f<\/em> e <em>g<\/em>"},"content":{"rendered":"<p><ul id='GTTabs_ul_14713' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14713' class='GTTabs_curr'><a  id=\"14713_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14713' ><a  id=\"14713_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_14713'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera as fun\u00e7\u00f5es <em>f<\/em> e <em>g<\/em>, definidas por \\(f\\left( x \\right) = {x^2}\\) e \\(g\\left( x \\right) = &#8211; 6x &#8211; 8\\).<br \/>\nDetermina\u00a0analiticamente as coordenadas dos pontos de interse\u00e7\u00e3o dos gr\u00e1ficos de <em>f<\/em> e <em>g<\/em>.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14713' onClick='GTTabs_show(1,14713)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14713'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Comecemos por determinar as abcissas dos pontos de interse\u00e7\u00e3o dos gr\u00e1ficos de <em>f<\/em> e <em>g<\/em>:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{f\\left( x \\right) = g\\left( x \\right)}&amp; \\Leftrightarrow &amp;{{x^2} = &#8211; 6x &#8211; 8}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} + 6x + 8 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; 6 \\mp \\sqrt {36 &#8211; 32} }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; 6 \\mp 2}}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 4}&amp; \\vee &amp;{x = &#8211; 2}\\end{array}}\\end{array}\\]<\/p>\n<p>Logo, as coordenadas dos pontos de interse\u00e7\u00e3o dos dois gr\u00e1ficos s\u00e3o:<\/p>\n<ul>\n<li>\\(\\left( { &#8211; 4,\\;f\\left( { &#8211; 4} \\right)} \\right) = \\left( { &#8211; 4,\\;16} \\right)\\)<\/li>\n<li>\\(\\left( { &#8211; 2,\\;f\\left( { &#8211; 2} \\right)} \\right) = \\left( { &#8211; 2,\\;4} \\right)\\).<\/li>\n<\/ul>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/2017-18-MF9P2-pag113-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14715\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14715\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/2017-18-MF9P2-pag113-7.png\" data-orig-size=\"694,405\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Gr\u00e1ficos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/2017-18-MF9P2-pag113-7.png\" class=\"aligncenter wp-image-14715 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/2017-18-MF9P2-pag113-7.png\" alt=\"\" width=\"694\" height=\"405\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/2017-18-MF9P2-pag113-7.png 694w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/2017-18-MF9P2-pag113-7-300x175.png 300w\" sizes=\"auto, (max-width: 694px) 100vw, 694px\" \/><\/a><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14713' onClick='GTTabs_show(0,14713)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera as fun\u00e7\u00f5es f e g, definidas por \\(f\\left( x \\right) = {x^2}\\) e \\(g\\left( x \\right) = &#8211; 6x &#8211; 8\\). Determina\u00a0analiticamente as coordenadas dos pontos de interse\u00e7\u00e3o dos gr\u00e1ficos&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20298,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,345,499,500],"series":[],"class_list":["post-14713","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-9-o-ano","tag-funcao-afim","tag-funcao-quadratica","tag-parabola"],"views":4172,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag113-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14713","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14713"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14713\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20298"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14713"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14713"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14713"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14713"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}