{"id":4467,"date":"2026-08-17T21:58:00","date_gmt":"2026-08-17T19:58:00","guid":{"rendered":"https:\/\/mxth.dk\/?p=4467"},"modified":"2026-08-17T22:02:34","modified_gmt":"2026-08-17T20:02:34","slug":"toppunkt-for-andengradsfunktionen","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=4467","title":{"rendered":"Toppunkt for andengradsfunktionen"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Toppunktet for andengradsfunktionen op formen $f(x)=ax^2+bx+c$ kan bestemmes ved <\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">$T=\\left(-\\dfrac{b}{2a},-\\dfrac{d}{4a}\\right)=\\left(-\\dfrac{b}{2a},-\\dfrac{b^2-4ac}{4a}\\right)$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">For andengradsfunktionen er x-v\u00e6rdien for toppunktet ogs\u00e5 x-v\u00e6rdien for symmetriaksen og derved er givet ved<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">$x=-\\dfrac{b}{2a}$<\/p>\n\n\n<h2 class=\" wp-block-heading eplus-wrapper eplus-styles-uid-4f3c87\">Opgaver<\/h2>\n\n\n<style>\n  table, th, td {\n    border: 1px solid black;\n    border-collapse: collapse;\n  }\n<\/style>\n<table width=\"100%\" border=\"1\">\n  <thead>\n    <tr>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#3CB371\">Gr\u00f8n<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#FFA500\">Gul<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#DC143C\">R\u00f8d<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/laerebogimatematik1hhx.systime.dk\/?id=262#c1409\" target=\"_blank\" rel=\"noopener noreferrer\">lim1hhx521<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/laerebogimatematik1hhx.systime.dk\/?id=262#c1414\" target=\"_blank\" rel=\"noopener noreferrer\">lim1hhx526<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/laerebogimatematik1hhx.systime.dk\/?id=262#c1412\" target=\"_blank\" rel=\"noopener noreferrer\">lim1hhx524<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/laerebogimatematik1hhx.systime.dk\/?id=262#c1410\" target=\"_blank\" rel=\"noopener noreferrer\">lim1hhx522<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/laerebogimatematik1hhx.systime.dk\/?id=262#c1413\" target=\"_blank\" rel=\"noopener noreferrer\">lim1hhx525<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/laerebogimatematik1hhx.systime.dk\/?id=262#c1411\" target=\"_blank\" rel=\"noopener noreferrer\">lim1hhx523<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/laerebogimatematik1hhx.systime.dk\/?id=262#c2973\" target=\"_blank\" rel=\"noopener noreferrer\">lim1hhx527<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Toppunktet for andengradsfunktionen op formen $f(x)=ax^2+bx+c$ kan bestemmes ved $T=\\left(-\\dfrac{b}{2a},-\\dfrac{d}{4a}\\right)=\\left(-\\dfrac{b}{2a},-\\dfrac{b^2-4ac}{4a}\\right)$ For andengradsfunktionen er x-v\u00e6rdien for toppunktet ogs\u00e5 x-v\u00e6rdien for symmetriaksen og derved er givet ved $x=-\\dfrac{b}{2a}$ Opgaver Gr\u00f8n Gul R\u00f8d lim1hhx521 lim1hhx526 lim1hhx524 lim1hhx522 lim1hhx525 lim1hhx523 lim1hhx527<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[33,12,41,40,3],"tags":[],"class_list":["post-4467","post","type-post","status-publish","format-standard","hentry","category-andengradspolynomium","category-funktioner","category-hhx","category-htx","category-matematik"],"featured_image_src":null,"author_info":{"display_name":"Henriksen","author_link":"https:\/\/mxth.dk\/?author=1"},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/4467","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4467"}],"version-history":[{"count":5,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/4467\/revisions"}],"predecessor-version":[{"id":4473,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/4467\/revisions\/4473"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}