{"id":727,"date":"2020-04-26T07:38:56","date_gmt":"2020-04-26T05:38:56","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=727"},"modified":"2021-11-20T11:22:15","modified_gmt":"2021-11-20T10:22:15","slug":"die-quadratische-funktion-yx%c2%b2","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=727","title":{"rendered":"Die quadratische Funktion y=x\u00b2"},"content":{"rendered":"\n<p class=\"has-white-color has-primary-background-color has-text-color has-background has-normal-font-size\"><strong>Die quadratische Funktion y=x\u00b2 <\/strong><br><br> Die Funktion y=x\u00b2 besitzt einen achsensymmetrischen Graphen, der den Scheitelpunkt (0|0) besitzt. Die Nullstelle der Funktion liegt ebenfalls bei (0|0) im Koordinatenursprung.  <\/p>\n\n\n\n<p>Die Funktion f\u00e4llt im Intervall (-\u221e ; 0 ) und steigt im Intervall  (0 ; \u221e).<\/p>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">Die Wertetabelle:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-subtle-pale-blue-background-color has-background\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">x<\/td><td class=\"has-text-align-center\" data-align=\"center\">-3<\/td><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\">0<\/td><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\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">y=x\u00b2<\/td><td class=\"has-text-align-center\" data-align=\"center\">(-3)*(-3) = <strong>9<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">(-2)*(-2) =<strong> 4<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">(-1)*(-1)=<strong>1<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">0*0= <strong>0<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">1*1=<strong>1<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">2*2=<strong>4<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">3*3=<strong>9<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">Der Graph der Funktion im Intervall (-2,8 ; 2,8)<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/04\/desmos-graph-1-1-1024x1024.png\" alt=\"\" class=\"wp-image-742\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/04\/desmos-graph-1-1-1024x1024.png 1024w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/04\/desmos-graph-1-1-300x300.png 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/04\/desmos-graph-1-1-150x150.png 150w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/04\/desmos-graph-1-1-768x768.png 768w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/04\/desmos-graph-1-1-1536x1536.png 1536w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/04\/desmos-graph-1-1-80x80.png 80w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/04\/desmos-graph-1-1.png 2000w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-white-color has-text-color has-background\" style=\"background-color:#ff0000\">Bearbeite die Funktion bei <a href=\"http:\/\/www.desmos.com\" target=\"_blank\" rel=\"noreferrer noopener\">www.desmos.com<\/a><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" src=\"https:\/\/www.desmos.com\/calculator\/wnrfllw6u3?embed\" width=\"500px\" height=\"500px\" style=\"border: 1px solid #ccc\" frameborder=\"0\"><\/iframe><\/pre>\n\n\n\n<p>Das Intervall (0;1) zeigt den nichtlinearen Verlauf der quadratischen Funktion y=x\u00b2.<br>Hier wachsen die Argumente zuerst schneller an als die Funktionswerte. Dies kehrt sich jedoch alsbald um. Im Punkt (1|1) sind Argument und Funktionswert gleich gro\u00df. Oberhalb  des Argumentes 1 nehmen dann die Funktionswerte rasant zu.<\/p>\n\n\n<p>[smartslider3 slider=&#8220;6&#8243;]<\/p>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_727\" class=\"pvc_stats all  \" data-element-id=\"727\" 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>Die quadratische Funktion y=x\u00b2 Die Funktion y=x\u00b2 besitzt einen achsensymmetrischen Graphen, der den Scheitelpunkt (0|0) besitzt. Die Nullstelle der Funktion liegt ebenfalls bei (0|0) im Koordinatenursprung. Die Funktion f\u00e4llt im Intervall (-\u221e ; 0 ) und steigt im Intervall (0 ; \u221e). Die Wertetabelle: x -3 -2 -1 0 1 2 3 y=x\u00b2 (-3)*(-3) = 9 (-2)*(-2) = 4 (-1)*(-1)=1<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_727\" class=\"pvc_stats all  \" data-element-id=\"727\" 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":[127,128,129,265,275,286],"class_list":["post-727","post","type-post","status-publish","format-standard","hentry","category-quadratische-funktion","category-quadratische-funktionen","tag-quadratisch","tag-quadratische-funktion","tag-x","tag-graph","tag-parabel","tag-achsensymmetrisch"],"a3_pvc":{"activated":true,"total_views":660,"today_views":0},"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/727","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=727"}],"version-history":[{"count":0,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/727\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=727"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=727"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=727"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}