Normalparabel

Wie sieht die einfachste quadratische Funktion aus?
Du hast gelernt, dass Funktionen, die ein [math]x^2[/math] im Funktionsterm haben, [b]quadratische Funktionen [/b]heißen. Logischerweise sieht dann die einfachste quadratische Funktion so aus: [math]y=f\left(x\right)=x^2[/math].[br][br]Sie wird [b]Normalparabel[/b] genannt. Diese Funktion wollen wir nun weiter untersuchen. Dazu erstellen wir eine Wertetabelle und zeichnen ihr Schaubild.
Übung zur Normalparabel
[quote][size=150][br]1.Quadratfunktion und Normalparabel[/size][size=150][size=100][br][br]Die einfachste quadratische Funktion hat die Gleichung [math]y=x^2[/math] [br]und heißt [b]Normalbarabel.[br][br]Berechne die fehlenden Werte der Wertetabelle[/b][/size][/size][b]:[br][br][img]data:image/png;base64,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[/img][/b][/quote]
Zeichne nun auch ein Schaubild dieser Funktion im folgenden Applet![br][br]Gib dazu den Funktionsterm oben links ein. [br]

Information: Normalparabel