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Zusammenfassung Alles rund um quadratische Funktionen $3.23   Add to cart
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Zusammenfassung Alles rund um quadratische Funktionen
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  • Course
  • Mathematik
  • Institution
  • Gymnasium

Dieses Dokument gibt dir einen kompakte Übersicht über alle wichtigen Eigenschaften einer quadratischen Funktion. Von der Darstellungsform bis hin zur eleganten Berechnung der Nullstelle ist hier alles mit dabei.

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Document information

  • June 23, 2023
  • 2
  • 2022/2023
  • Summary

Subjects

  • quadratische funktionen
  • nullstellen
  • symmetrie
  • schaubild
  • scheitelpunktform
  • monotonie

Written for

  • Secondary school
  • Gymnasium
  • Mathematik
  • 1
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Die quadratische Funktion


Allgemeine Form

𝑓(𝑥) = 𝑎𝑥2 + 𝑏𝑥 + 𝑐


Scheitelpunktform
2
𝑏 𝑏
𝑓(𝑥) = 𝑎 ⋅ (𝑥 + 𝑑)2 + 𝑒 mit 𝑑 = 2𝑎 und 𝑒 = − 4𝑎 +𝑐

Verwende immer die Scheitelpunktform, denn mit 𝑎, 𝑑 und 𝑒 kannst du alle wich-
INFO-CIRCLE tigen Informationen direkt ableiten und den Funktionsgraph schnell zeichnen.


Beispiele von Funktionsgraphen

𝑦
𝑓(𝑥) = (𝑥 + 1)2 − 1

3
ℎ(𝑥) = 0,3 ⋅ (𝑥 + 2)2 − 4
2 𝑆𝑔

1

𝑥
−4 −3 −2 −1 0 1 2 3 4
−1
𝑆𝑓
−2
𝑔(𝑥) = −4 ⋅ (𝑥 − 3)2 + 1,5
−3

−4
𝑆ℎ



Stauchung oder Streckung

• Für |𝑎| < 1 ist der Graph der Funktion gestaucht.
• Für |𝑎| > 1 ist der Graph der Funktion gestreckt.




1

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