{"id":768,"date":"2020-04-26T13:27:02","date_gmt":"2020-04-26T11:27:02","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=768"},"modified":"2024-07-15T07:33:35","modified_gmt":"2024-07-15T05:33:35","slug":"die-quadratische-funktion-yax%c2%b2","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=768","title":{"rendered":"Die quadratische Funktion y=ax\u00b2"},"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>Der Koeffizient(Faktor) a f\u00fcr zu einer Streckung oder Stauchung der Normalparabel der Funktion y=x\u00b2. Ist der Faktor zudem noch negativ, so bedeutet dies die Spiegelung  des Graphen an der x-Achse(Abzisse).<\/p>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\"><strong>y=ax\u00b2 mit a&gt;1<\/strong> f\u00fchren zur Streckung des Graphen Beispiele hier sind y = 2x\u00b2 oder y = 5,7x\u00b2<\/p>\n\n\n\n<p>Die <span style=\"color:#ff0000\" class=\"has-inline-color\">Normalparabel y = x\u00b2<\/span>  ist hier <span style=\"color:#ff0202\" class=\"has-inline-color\">rot <\/span>dargestellt.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" src=\"https:\/\/www.desmos.com\/calculator\/cw2xq7hf6v?embed\" width=\"500px\" height=\"500px\" style=\"border: 1px solid #ccc\" frameborder=\"0\"><\/iframe><\/pre>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\"><strong>y=ax\u00b2 mit a&lt;1<\/strong> f\u00fchren zur <strong>Stauchung<\/strong>  des Graphen Beispiele hier sind y = 0,5x\u00b2 oder y = 0,07x\u00b2<\/p>\n\n\n\n<p>Die <span style=\"color:#ff0000\" class=\"has-inline-color\">Normalparabel y = x\u00b2<\/span>  ist hier <span style=\"color:#ff0202\" class=\"has-inline-color\">rot <\/span>dargestellt.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" src=\"https:\/\/www.desmos.com\/calculator\/dnznjkqroq?embed\" width=\"500px\" height=\"500px\" style=\"border: 1px solid #ccc\" frameborder=\"0\"><\/iframe><\/pre>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Setzt man f\u00fcr a negative Werte ein, so entsteht ein Graph, der im 3. und 4. Quadranten verl\u00e4uft und nach unten ge\u00f6ffnet ist.<\/p>\n\n\n\n<p>Die <span style=\"color:#ff0000\" class=\"has-inline-color\">rot<\/span> gezeichnete Funktion hei\u00dft <span style=\"color:#ff0000\" class=\"has-inline-color\">y =  \u2013 x\u00b2<\/span>.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" src=\"https:\/\/www.desmos.com\/calculator\/mmvzm5zbmr?embed\" width=\"500px\" height=\"500px\" style=\"border: 1px solid #ccc\" frameborder=\"0\"><\/iframe><\/pre>\n\n\n\n<p class=\"has-white-color has-text-color has-background\" style=\"background-color:#ec2222\"><strong>Klick in das untere  Fenster um auf desmos.com  mit dem REGLER f\u00fcr a die unterschiedlichen Effekte auf den  Funktionsgraph von y= ax\u00b2 auszuprobieren.<\/strong><\/p>\n\n\n\n<iframe loading=\"lazy\" scrolling=\"no\" title=\"Die Funktion y=f(x)=ax\u00b2\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/s7yf9sfv\/width\/724\/height\/562\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/false\/rc\/false\/ld\/true\/sdz\/true\/ctl\/false\" width=\"724px\" height=\"562px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe>\n\n\n\n<iframe loading=\"lazy\" scrolling=\"no\" title=\"ax\u00b2\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/ptqwb2vr\/width\/726\/height\/564\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/false\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"726px\" height=\"564px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_768\" class=\"pvc_stats all  \" data-element-id=\"768\" 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>Der Koeffizient(Faktor) a f\u00fcr zu einer Streckung oder Stauchung der Normalparabel der Funktion y=x\u00b2. Ist der Faktor zudem noch negativ, so bedeutet dies die Spiegelung des Graphen an der x-Achse(Abzisse). y=ax\u00b2 mit a&gt;1 f\u00fchren zur Streckung des Graphen Beispiele hier sind y = 2x\u00b2 oder y = 5,7x\u00b2 Die Normalparabel y = x\u00b2 ist hier rot dargestellt. y=ax\u00b2 mit a&lt;1<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_768\" class=\"pvc_stats all  \" data-element-id=\"768\" 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":[127,128,265,275,276,277],"class_list":["post-768","post","type-post","status-publish","format-standard","hentry","category-quadratische-funktion","category-quadratische-funktionen","tag-quadratisch","tag-quadratische-funktion","tag-graph","tag-parabel","tag-streckung","tag-stauchung"],"a3_pvc":{"activated":true,"total_views":901,"today_views":0},"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/768","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=768"}],"version-history":[{"count":1,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/768\/revisions"}],"predecessor-version":[{"id":8397,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/768\/revisions\/8397"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=768"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=768"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=768"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}