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Auf der letzten Kursseite findest du auch einen Direktlink."}]}],"id":"6b071c83-2a7c-483a-bcc6-46075c77bb68"}],"id":"87421994-b436-44f4-8d3a-ca120101787c"},"id":"19229-course-page","title":"Übungsaufgaben"},{"content":{"plugin":"rows","state":[{"plugin":"text","state":[{"type":"p","children":[{"text":"Überlege jetzt, welche Auswirkungen der Parameter "},{"type":"math","src":"a","inline":true,"children":[{"text":"a"}]},{"text":" auf die Parabel haben könnte? Was bleibt noch übrig?"}]},{"type":"p","children":[{"text":"Auch hier kannst du als persönliche Übung wieder den Graphen der Funktion "},{"type":"math","src":"ax^2","inline":true,"children":[{"text":"ax^2"}]},{"text":" für verschiedene "},{"type":"math","src":"a","inline":true,"children":[{"text":"a"}]},{"text":" zeichnen."}]}],"id":"06c154ab-47b4-483a-9b14-f551075b89cd"},{"plugin":"spoiler","state":{"title":"Lösung und Anschauung","content":{"plugin":"rows","state":[{"plugin":"text","state":[{"type":"p","children":[{"text":"Der Parameter "},{"type":"math","src":"a","inline":true,"children":[{"text":"a"}]},{"text":" gibt an, ob die Parabel nach oben oder nach unten geöffnet ist und wie stark die Parabel gestreckt bzw. gestaucht ist."}]},{"type":"p","children":[{"text":"Ist "},{"type":"math","src":"a>0","inline":true,"children":[{"text":"a>0"}]},{"text":", dann ist die Parabel nach oben geöffnet."}]},{"type":"p","children":[{"text":"Ist "},{"type":"math","src":"a<0","inline":true,"children":[{"text":"a<0"}]},{"text":", dann ist die Parabel nach unten geöffnet, dabei wird die nach oben geöffnete Parabel an einer Parallelen zur "},{"type":"math","src":"x","inline":true,"children":[{"text":"x"}]},{"text":"-Achse durch den Scheitel gespiegelt (Falls der Scheitel - wie hier noch - auf der "},{"type":"math","src":"x","inline":true,"children":[{"text":"x"}]},{"text":"-Achse liegt wird einfach an dieser Achse gespiegelt)."}]},{"type":"p","children":[{"text":"Ist "},{"type":"math","src":"|a|>1","inline":true,"children":[{"text":"|a|>1"}]},{"text":", so wird die Parabel gestreckt, d.h. der Funktionsgraph ist schmäler als die Normalparabel."}]},{"type":"p","children":[{"text":"Ist "},{"type":"math","src":"|a|<1","inline":true,"children":[{"text":"|a|<1"}]},{"text":" so wird die Parabel gestaucht, d.h. der Funktionsgraph ist breiter als die Normalparabel"}]}],"id":"87db7afa-7c56-407b-8770-4fdfdc6251af"},{"plugin":"image","state":{"src":"https://assets.serlo.org/legacy/8921_hKX0cKDYYa.png","alt":"legacy geogebra formula","caption":{"plugin":"text","state":[{"type":"p","children":[{}]}],"id":"8fb39fe8-1a51-4ad1-b6bf-066ae532dea6"}},"id":"2a6add43-2d51-497a-994f-13d44fe73a63"},{"plugin":"text","state":[{"type":"p","children":[{"text":"Da es sich hier nicht mehr um eine Normalparabel handelt, kann man die Parabel nicht mehr einfach (z.B. mit einer Parabelschablone) zeichnen. 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