{"id":770,"date":"2020-04-26T13:44:46","date_gmt":"2020-04-26T11:44:46","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=770"},"modified":"2024-07-15T07:33:38","modified_gmt":"2024-07-15T05:33:38","slug":"die-scheitelpunktsform-der-quadratischen-funktion","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=770","title":{"rendered":"Die Scheitelpunktform der quadratischen Funktion"},"content":{"rendered":"\n<p><img loading=\"lazy\" decoding=\"async\" width=\"50\" height=\"50\" class=\"wp-image-7501\" style=\"width: 50px;\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2.png\" alt=\"\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2.png 100w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2-80x80.png 80w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2-50x50.png 50w\" sizes=\"auto, (max-width: 50px) 100vw, 50px\" \/><\/p>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background has-medium-font-size\">y = (x+d)\u00b2 +e<\/p>\n\n\n\n<p>Schau dir den Einfluss von <span class=\"has-inline-color has-primary-color\"><strong>d<\/strong>(blau)<\/span> und <strong><span style=\"color:#28b709\" class=\"has-inline-color\">e(gr\u00fcn<\/span>)<\/strong> im folgenden Plotterfenster an. <\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" scrolling=\"no\" title=\"Verschiebung kombiniert\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/TIHOAswd\/width\/697\/height\/376\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/true\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"697px\" height=\"376px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe><\/pre>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">Autor: Eckerts, geogebra.org<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#fbffcb\">Stell f\u00fcr <strong>d = 2<\/strong> ein und w\u00e4hle f\u00fcr <strong>e  = \u2013 3<\/strong>. Lies den Scheitelpunkt ab und notiere ihn!<br>Verfahre mit einigen ganzzahligen  Beispielen ebenso.<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>d<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>e<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">S <\/td><td><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-4<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><td class=\"has-text-align-center\" data-align=\"center\">-4<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-white-color has-text-color has-background has-normal-font-size\" style=\"background-color:#ff1e70\">Die Form y = (x+d)\u00b2 + e hei\u00dft Scheitelpunktsform, da der Scheitelpunkt mit seinen Koordinaten -d und e schon in der Vorschrift enthalten ist..<\/p>\n\n\n\n<p class=\"has-text-align-center has-background has-medium-font-size\" style=\"background-color:#f9e957\">Der Scheitelpunkt dieser Funktion liegt bei S(-d|e)<br>Der Graph ist immer eine Normalparabel.<\/p>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Hier noch mal ein voreingestellter Plotter auf www.desmos.com<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" src=\"https:\/\/www.desmos.com\/calculator\/1ngehpjsj4?embed\" width=\"500px\" height=\"500px\" style=\"border: 1px solid #ccc\" frameborder=\"0\"><\/iframe><\/pre>\n\n\n\n<iframe loading=\"lazy\" scrolling=\"no\" title=\"Nullstellen und Scheitelpunkt\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/bxfapwtc\/width\/1200\/height\/800\/border\/888888\/sfsb\/true\/smb\/true\/stb\/false\/stbh\/false\/ai\/true\/asb\/false\/sri\/true\/rc\/true\/ld\/true\/sdz\/false\/ctl\/false\" width=\"1200px\" height=\"800px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_770\" class=\"pvc_stats all  \" data-element-id=\"770\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p><div class=\"pvc_clear\"><\/div> ","protected":false},"excerpt":{"rendered":"<p>y = (x+d)\u00b2 +e Schau dir den Einfluss von d(blau) und e(gr\u00fcn) im folgenden Plotterfenster an. Autor: Eckerts, geogebra.org Stell f\u00fcr d = 2 ein und w\u00e4hle f\u00fcr e = \u2013 3. Lies den Scheitelpunkt ab und notiere ihn!Verfahre mit einigen ganzzahligen Beispielen ebenso. d e S 2 -1 -4 2 3 -4 -1 2 Die Form y = (x+d)\u00b2<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_770\" class=\"pvc_stats all  \" data-element-id=\"770\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[966,54],"tags":[127,128,265,275],"class_list":["post-770","post","type-post","status-publish","format-standard","hentry","category-quadratische-funktion","category-quadratische-funktionen","tag-quadratisch","tag-quadratische-funktion","tag-graph","tag-parabel"],"a3_pvc":{"activated":true,"total_views":651,"today_views":0},"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/770","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=770"}],"version-history":[{"count":1,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/770\/revisions"}],"predecessor-version":[{"id":8398,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/770\/revisions\/8398"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}