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Von Version 32.1
bearbeitet von Holger Engels
am 2025/11/18 07:49
Änderungskommentar: Neues Bild Arithmagon Parabel Formen.svg hochladen
Auf Version 4.1
bearbeitet von akukin
am 2025/05/23 12:12
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Titel
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1 -BPE 8.4 Darstellungsformen, Achsenschnittpunkte
1 +BPE_8_4
Dokument-Autor
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1 -XWiki.holgerengels
1 +XWiki.akukin
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="I" kompetenzen="K3,K4,K5" quelle="Slavko Lamp, Bastian Knöpfle" zeit="8" cc="by-sa"}}
9 -
8 +{{aufgabe id="Scheitelpunkt " afb="I" kompetenzen="" quelle="Team Mathebrücke" zeit="" cc="by-sa" tags="mathebrücke"}}
9 +Begründe, welche der folgenden Behauptungen wahr oder falsch sind.
10 10  (%class=abc%)
11 -1. Eine nach oben geöffnete Parabel mit dem Scheitelpunkt P(3|4) schneidet die x-Achse nicht.
12 -Gib eine mögliche Funktionsgleichung in Scheitlform und Hauptform an.
13 -1. Eine nach unten geöffnete Parabel mit dem Scheitelpunkt P(5|9) schneidet die x-Achse zwei Mal.
14 -Gib eine mögliche Funktionsgleichung in Scheitelform und Linearfaktorform an.
15 -{{/aufgabe}}
11 +1. Eine nach oben geöffnete Parabel mit dem Scheitelpunkt P(3|4) schneidet die x-Achse nicht.
12 +1. Eine nach unten geöffnete Parabel mit dem Scheitelpunkt P(15|30) schneidet die x-Achse zwei Mal.
16 16  
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]]
20 -{{/aufgabe}}
14 +{{lehrende}}
15 +**Sinn dieser Aufgabe:**
16 +Zusammenhang zwischen Scheitelpunkt, Verlauf und Schnittpunkte mit der x-Achse erklären.
17 +{{/lehrende}}
21 21  
22 -{{aufgabe id="Verfahrensauswahl" afb="II" kompetenzen="K1,K4,K5" quelle="Simone Hochrein" zeit="11" cc="by-sa" tags=""}}
23 -Je nach Art der gegebenen Informationen ist die Scheitelform oder die Linearfaktorform besonders geeignet zum Aufstellen der Funktionsgleichung. Begründe jeweils, welche Form bei den im Folgenden gegebenen Informationen zum Aufstellen der Funktionsgleichung geeignet ist.
24 -(%class=abc%)
25 -1. Der Graph der Funktion schneidet die x-Achse bei {{formula}}-3{{/formula}} und {{formula}}2{{/formula}} und die y-Achse bei {{formula}}-3{{/formula}}.
26 -1. Der Scheitel der Funktion liegt bei {{formula}}S(2|4){{/formula}}, der Streckfaktor ist {{formula}}a=-2{{/formula}}.
27 -1. Der Scheitel liegt bei {{formula}}S(3|1){{/formula}}, der Punkt {{formula}}A(5|2){{/formula}} liegt auf dem Graphen der Funktion.
28 -1. Der Graph der Funktion hat sein Maximum bei {{formula}}S(0|2){{/formula}}, er schneidet die x-Achse bei {{formula}}x_1=3{{/formula}}.
29 -1. (((Folgende Wertetabelle gehört zur Funktion.
30 -(% class="border" style="table-layout: fixed; text-align:center" %)
31 -|{{formula}}x{{/formula}}|0|1|2|3|4
32 -|{{formula}}f(x){{/formula}}|5|3,5|3|3,5|5)))
33 -1. (((Der Graph der Funktion ist in folgender Abbildung dargestellt.
34 -[[image:8.4 - A4.svg||width="450" ]])))
35 35  {{/aufgabe}}
36 36  
37 -{{aufgabe id="Funktionsterm bestimmen" afb="II" kompetenzen="K4,K5" quelle="Simone Hochrein" zeit="11" cc="by-sa" tags=""}}
38 -Bestimme die Funktionsterme zur vorangegangenen Aufgabe mit dem jeweils gewählten Verfahren.
39 -{{/aufgabe}}
40 -
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 -
21 +{{aufgabe id="Abschnittsweise definierte Funktionen" afb="II" kompetenzen="" quelle="Team Mathebrücke" zeit="" cc="by-sa" tags="mathebrücke"}}
22 +[[image:AbschnittsweisedefinierteFunktion.png||width="350" style="display:block;margin-left:auto;margin-right:auto"]]
48 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 -
53 -{{aufgabe id="Abschnittsweise definierte Funktionen" afb="II" kompetenzen="K4,K5" quelle="Team Mathebrücke" zeit="4" cc="by-sa" tags="mathebrücke"}}
54 -[[image:AbschnittsweisedefinierteFunktion.png||width="450" style="display:block;margin-left:auto;margin-right:auto"]]
55 -(%class=abc%)
56 56  1. Lies folgende Funktionswerte ab:
57 57  {{formula}}f(0) = {{/formula}}
58 58  {{formula}}f(3,5) = {{/formula}}
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60 60  {{formula}}f(2) = {{/formula}}
61 61  1. An welchen Stellen gilt {{formula}}y = 4{{/formula}}?
62 62  1. Gib die zugehörigen Gleichungen der Funktion an.
63 -{{comment}}
31 +
32 +{{lehrende}}
64 64  **Sinn dieser Aufgabe:**
65 65  Umgang mit Diagrammen
66 -{{/comment}}
35 +{{/lehrende}}
36 +
67 67  {{/aufgabe}}
68 68  
69 -{{seitenreflexion bildungsplan="5" kompetenzen="4" anforderungsbereiche="5" kriterien="5" menge="5"/}}
39 +{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
40 +
8.4 - A4.svg
Author
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1 -XWiki.simonehochrein
Größe
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1 -16.4 KB
Inhalt
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Arithmagon Parabel Formen.svg
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