{"media":{"type":{"params":{"contentName":"Bild","alt":"Parabel","file":{"path":"images\/file-5ff0a0b54d7a5.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":595,"height":418}},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"CC BY-SA","title":"Parabel","authors":[{"name":"Graf Zahl","role":"Author"}],"licenseVersion":"4.0","source":"https:\/\/www.geogebra.org\/?lang=de"},"subContentId":"96f8bad5-ab41-44ba-a852-5cdb69c47fc8"},"disableImageZooming":false},"answers":[{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"

Richtig. Sehr gut.<\/div>\n","notChosenFeedback":""},"text":"

f'(x) = 2x-8; x_{E<\/sub>=4 f(4) = 4^{2<\/sup>-8*4+14 = -2 S(4;-2)<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"f'(x) = 8x-2; x_{E<\/sub>=0,25 f(4) = 0,25^{2<\/sup>-8*0,25+14 = ca. 12,1 S(4;-2)<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":true,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Hinweis anzeigen","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","tipAvailable":"Hinweis verf\u00fcgbar","feedbackAvailable":"R\u00fcckmeldung verf\u00fcgbar","readFeedback":"R\u00fcckmeldung vorlesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Richtige Antwort","shouldCheck":"H\u00e4tte gew\u00e4hlt werden m\u00fcssen","shouldNotCheck":"H\u00e4tte nicht gew\u00e4hlt werden sollen","noInput":"Bitte antworte, bevor du die L\u00f6sung ansiehst"},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"Leiten Sie die Gleichung der Parabel her, indem Sie den Scheitelpunkt ablesen und die Parabelgleichung in der Scheitelpunktform darstellen. \u00dcberpr\u00fcfen Sie die Koordinaten des Scheitelpunktes mithilfe der ertsen Ableitung f'(x) und zweiten Ableitung f''(x) und den notwendigen und hinreichenden Bedingungen f\u00fcr Extremwerte. W\u00e4hlen Sie dann die richtige L\u00f6sung aus.<\/p>\n"}}}}}