Schnittpunkt Zweier Parabeln Beispiel Essay

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Gegeben sind die Funktionsgleichungen zweier Parabeln, von denen die Schnittpunkte zu bestimmen sind.

Soll der Schnittpunkt der Graphen zweier Funktionen bestimmt werden, so setzt man die Funktionsgleichungen gleich. Das galt schon für die Schnittpunkte von Geraden und Gerade und Parabel. Dieses Verfahren wendet man auch bei zwei Parabeln an.


Bestimmen Sie die Schnittpunkte folgender Parabeln und zeichnen Sie die Graphen.

Schnittpunkt zweier Parabeln   Interaktiv: Nach Eingabe der Koeffizienten beider Funktionsgleichungen, werden die Schnittpunkte berechnet, dann können beide Graphen gezeichnet werden.


Es gibt zwei Schnittpunkte,
denn D> 0. 


Es gibt nur einen Berührungspunkt,
denn D = 0. 


Es gibt keinen Schnittpunkt,
denn D < 0. 


Führt das Gleichsetzen von f(x) und g(x) auf eine lineare Gleichung, so haben beide Parabeln nur einen Schnittpunkt.

Aus dem Übungsbeispiel erkennen wir, das die Anzahl der Schnittpunkte, die zwei Parabeln miteinander haben direkt aus der Diskriminante ablesbar ist.

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