{"id":14675,"date":"2018-04-19T08:48:20","date_gmt":"2018-04-19T07:48:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14675"},"modified":"2022-01-09T22:40:54","modified_gmt":"2022-01-09T22:40:54","slug":"uma-funcao-quadratica-representada-graficamente","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14675","title":{"rendered":"Uma fun\u00e7\u00e3o quadr\u00e1tica representada graficamente"},"content":{"rendered":"<p><ul id='GTTabs_ul_14675' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14675' class='GTTabs_curr'><a  id=\"14675_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14675' ><a  id=\"14675_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_14675'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14676\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14676\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7.png\" data-orig-size=\"413,335\" 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\/9V2Pag110-7.png\" class=\"alignright size-medium wp-image-14676\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7-300x243.png\" alt=\"\" width=\"300\" height=\"243\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7-300x243.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7.png 413w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Considera uma fun\u00e7\u00e3o <em>f<\/em> quadr\u00e1tica representada graficamente no referencial cartesiano da figura por uma par\u00e1bola de eixo vertical e que passa na origem.<\/p>\n<p>Sabendo que o ponto de coordenadas \\(\\left( { &#8211; 2,\\; &#8211; 1} \\right)\\) pertence ao gr\u00e1fico de <em>f<\/em>, determina a express\u00e3o alg\u00e9brica de <em>f<\/em>.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14675' onClick='GTTabs_show(1,14675)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14675'>\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\/9V2Pag110-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14676\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14676\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7.png\" data-orig-size=\"413,335\" 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\/9V2Pag110-7.png\" class=\"alignright size-medium wp-image-14676\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7-300x243.png\" alt=\"\" width=\"300\" height=\"243\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7-300x243.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7.png 413w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Como o ponto de coordenadas \\(\\left( { &#8211; 2,\\; &#8211; 1} \\right)\\) pertence ao gr\u00e1fico de <em>f<\/em>, ent\u00e3o as suas coordenadas t\u00eam de verificar \\(f\\left( x \\right) = a{x^2}\\), com\u00a0\\(a \\ne 0\\).<\/p>\n<p>Assim, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{f\\left( { &#8211; 2} \\right) = &#8211; 1}&amp; \\Leftrightarrow &amp;{a \\times {{\\left( { &#8211; 2} \\right)}^2} = &#8211; 1}\\\\{}&amp; \\Leftrightarrow &amp;{4a = &#8211; 1}\\\\{}&amp; \\Leftrightarrow &amp;{a = &#8211; \\frac{1}{4}}\\end{array}\\]<\/p>\n<p>Portanto, a fun\u00e7\u00e3o <em>f<\/em> pode ser definida por\u00a0\\(f\\left( x \\right) = &#8211; \\frac{1}{4}{x^2}\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14675' onClick='GTTabs_show(0,14675)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera uma fun\u00e7\u00e3o f quadr\u00e1tica representada graficamente no referencial cartesiano da figura por uma par\u00e1bola de eixo vertical e que passa na origem. Sabendo que o ponto de coordenadas \\(\\left( {&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14677,"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],"series":[],"class_list":["post-14675","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"],"views":3133,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag110-7a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14675","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=14675"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14675\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14677"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14675"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14675"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14675"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}