{"id":14698,"date":"2018-04-19T19:27:32","date_gmt":"2018-04-19T18:27:32","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14698"},"modified":"2022-01-09T22:51:32","modified_gmt":"2022-01-09T22:51:32","slug":"uma-parabola-de-eixo-vertical-e-vertice-na-origem","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14698","title":{"rendered":"Uma par\u00e1bola de eixo vertical e v\u00e9rtice na origem"},"content":{"rendered":"<p><ul id='GTTabs_ul_14698' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14698' class='GTTabs_curr'><a  id=\"14698_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14698' ><a  id=\"14698_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_14698'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14699\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14699\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4.png\" data-orig-size=\"458,418\" 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\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4.png\" class=\"alignright size-medium wp-image-14699\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4-300x274.png\" alt=\"\" width=\"300\" height=\"274\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4-300x274.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4.png 458w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>A fun\u00e7\u00e3o <em>g<\/em> est\u00e1 representada graficamente no referencial cartesiano da figura por uma par\u00e1bola de eixo vertical e que passa na origem.<br \/>\nO ponto \\(A\\left( { &#8211; 2,\\;2} \\right)\\) pertence ao gr\u00e1fico de <em>g<\/em>.<\/p>\n<p>Determina uma express\u00e3o alg\u00e9brica de <em>g<\/em>.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14698' onClick='GTTabs_show(1,14698)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14698'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Os gr\u00e1ficos das fun\u00e7\u00f5es do tipo\u00a0\\(f\\left( x \\right) = a{x^2}\\), com\u00a0\\(a \\ne 0\\), s\u00e3o <strong>par\u00e1bolas de eixo vertical e v\u00e9rtice na origem<\/strong>.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14699\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14699\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4.png\" data-orig-size=\"458,418\" 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\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4.png\" class=\"alignright size-medium wp-image-14699\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4-300x274.png\" alt=\"\" width=\"300\" height=\"274\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4-300x274.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4.png 458w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Como o\u00a0ponto \\(A\\left( { &#8211; 2,\\;2} \\right)\\) pertence ao gr\u00e1fico de <em>g<\/em>, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{g\\left( { &#8211; 2} \\right) = 2}&amp; \\Leftrightarrow &amp;{a \\times {{\\left( { &#8211; 2} \\right)}^2} = 2}\\\\{}&amp; \\Leftrightarrow &amp;{4a = 2}\\\\{}&amp; \\Leftrightarrow &amp;{a = \\frac{1}{2}}\\end{array}\\]<\/p>\n<p>Logo, \\(g\\left( x \\right) = \\frac{1}{2}{x^2}\\) \u00e9 uma express\u00e3o alg\u00e9brica de <em>g<\/em>.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14698' onClick='GTTabs_show(0,14698)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A fun\u00e7\u00e3o g est\u00e1 representada graficamente no referencial cartesiano da figura por uma par\u00e1bola de eixo vertical e que passa na origem. O ponto \\(A\\left( { &#8211; 2,\\;2} \\right)\\) pertence ao&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14700,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,499,500],"series":[],"class_list":["post-14698","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-quadratica","tag-parabola"],"views":2516,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag112-4b.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14698","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=14698"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14698\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14700"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14698"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}