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Zuletzt geändert von majaseiboth am 2025/11/18 08:17
Von Version 27.1
bearbeitet von Bastian Knöpfle
am 2025/11/17 14:48
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Auf Version 34.1
bearbeitet von majaseiboth
am 2025/11/18 08:17
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Dokument-Autor
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1 -XWiki.bastianknoepfle
1 +XWiki.majaseiboth
Inhalt
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5 5  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann grafisch und rechnerisch den Scheitelpunkt und die Achsenschnittpunkte von Parabeln ermitteln.
6 6  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Gleichungen von Parabeln in Scheitel- oder gegebenenfalls Linearfaktorform bestimmen.
7 7  
8 -{{aufgabe id="Scheitelpunkt " afb="II" kompetenzen="K3,K4,K5" quelle="Slavko Lamp, Bastian Knöpfle" zeit="8" cc="by-sa"}}
8 +{{aufgabe id="Scheitelpunkt " afb="I" kompetenzen="K3,K4,K5" quelle="Slavko Lamp, Bastian Knöpfle" zeit="8" cc="by-sa"}}
9 9  
10 10  (%class=abc%)
11 11  1. Eine nach oben geöffnete Parabel mit dem Scheitelpunkt P(3|4) schneidet die x-Achse nicht.
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14 14  Gib eine mögliche Funktionsgleichung in Scheitelform und Linearfaktorform an.
15 15  {{/aufgabe}}
16 16  
17 -
18 -
19 -{{aufgabe id="Darstellungsformen" afb="II" kompetenzen="K1, K4, K5" quelle="Simone Hochrein" zeit="6" cc="by-sa" tags=""}}
20 -Die Funktionsgleichung einer quadratischen Funktion kann auf drei verschiedene Arten dargestellt werden:
21 -(% class="border" %)
22 -|Scheitelform|{{formula}}f(x)=a\cdot(x-x_S)^2+y_S{{/formula}}
23 -|Linearfaktorform|{{formula}}f(x)=a\cdot(x-x_1)(x-x_2){{/formula}}
24 -|Hauptform|{{formula}}f(x)=ax^2+bx+c{{/formula}}
25 -
26 -(%class=abc%)
27 -1. Gib die Anzahl der unbekannten Parameter an und benenne diese.
28 -1. Begründe, warum die Angabe von Scheitel und einem weiteren Punkt zur Aufstellung einer Funktionsgleichung ausreichend ist.
17 +{{aufgabe id="Arithmagon Parabel Formen" afb="I" kompetenzen="K4, K5" quelle="Martina Wagner" zeit="5"}}
18 +Ermittle, welche Zahlen in die leeren Kästchen in den Parabelgleichungen eingetragen werden müssen. Gib in den blauen Kästchen an, wie man von der einen zur anderen Darstellungsform kommt.
19 +[[image:Arithmagon Parabel Formen.svg||width=500 style=float:left]]
29 29  {{/aufgabe}}
30 30  
31 31  {{aufgabe id="Verfahrensauswahl" afb="II" kompetenzen="K1,K4,K5" quelle="Simone Hochrein" zeit="11" cc="by-sa" tags=""}}
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43 43  [[image:8.4 - A4.svg||width="450" ]])))
44 44  {{/aufgabe}}
45 45  
46 -{{aufgabe id="Funktionsterm bestimmen" afb="I" kompetenzen="K4,K5" quelle="Simone Hochrein" zeit="11" cc="by-sa" tags=""}}
37 +{{aufgabe id="Funktionsterm bestimmen" afb="II" kompetenzen="K4,K5" quelle="Simone Hochrein" zeit="11" cc="by-sa" tags=""}}
47 47  Bestimme die Funktionsterme zur vorangegangenen Aufgabe mit dem jeweils gewählten Verfahren.
48 48  {{/aufgabe}}
49 49  
41 +{{aufgabe id="Darstellungsformen" afb="III" kompetenzen="K1, K4, K5" quelle="Simone Hochrein" zeit="6" cc="by-sa" tags=""}}
42 +Die Funktionsgleichung einer quadratischen Funktion kann auf drei verschiedene Arten dargestellt werden:
43 +(% class="border" %)
44 +|Scheitelform|{{formula}}f(x)=a\cdot(x-x_S)^2+y_S{{/formula}}
45 +|Linearfaktorform|{{formula}}f(x)=a\cdot(x-x_1)(x-x_2){{/formula}}
46 +|Hauptform|{{formula}}f(x)=ax^2+bx+c{{/formula}}
47 +
48 +(%class=abc%)
49 +1. Gib die Anzahl der unbekannten Parameter an und benenne diese.
50 +1. Begründe, warum die Angabe von Scheitel und einem weiteren Punkt zur Aufstellung einer Funktionsgleichung ausreichend ist.
51 +{{/aufgabe}}
52 +
50 50  {{aufgabe id="Abschnittsweise definierte Funktionen" afb="II" kompetenzen="K4,K5" quelle="Team Mathebrücke" zeit="4" cc="by-sa" tags="mathebrücke"}}
51 51  [[image:AbschnittsweisedefinierteFunktion.png||width="450" style="display:block;margin-left:auto;margin-right:auto"]]
52 52  (%class=abc%)
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57 57  {{formula}}f(2) = {{/formula}}
58 58  1. An welchen Stellen gilt {{formula}}y = 4{{/formula}}?
59 59  1. Gib die zugehörigen Gleichungen der Funktion an.
60 -
61 -{{lehrende}}
63 +{{comment}}
62 62  **Sinn dieser Aufgabe:**
63 63  Umgang mit Diagrammen
64 -{{/lehrende}}
66 +{{/comment}}
65 65  {{/aufgabe}}
66 66  
67 -{{seitenreflexion bildungsplan="3" kompetenzen="3" anforderungsbereiche="3" kriterien="5" menge="3"/}}
69 +{{seitenreflexion bildungsplan="5" kompetenzen="4" anforderungsbereiche="5" kriterien="5" menge="5"/}}
Arithmagon Parabel Formen.svg
Author
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1 +XWiki.holgerengels
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Inhalt
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