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Änderungen von Dokument BPE 3.1 Eigenschaften und Formen

Zuletzt geändert von Holger Engels am 2025/04/09 13:57
Von Version 125.1
bearbeitet von Holger Engels
am 2024/12/18 14:18
Änderungskommentar: Neuen Anhang Vielfachheiten.ggb hochladen
Auf Version 140.2
bearbeitet von Holger Engels
am 2025/04/02 10:12
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

Seiteneigenschaften
Inhalt
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13 13  Input: Vorgegebene Schaubilder vergleichen (Gemeinsamkeiten, Unterschiede)
14 14  "Beschreiben": Form 'fühlen' (Globalverhalten, Lokalverhalten); vgl. Buchstaben-Formen (N, W) Nulltellentypen (einfach vs mehrfach (gerade vs ungerade))
15 15  
16 +{{lehrende}}
17 +**Unterrichtsidee** [[Eingangsklasse.BPE_3_1.Stufenpyramiden zur Faktorisierung von Polynomfunktionen.WebHome]]
18 +{{/lehrende}}
19 +
16 16  {{lernende}}
17 17  [[Nullstellen und Vielfachheiten interaktiv>>https://kmap.eu/app/browser/Mathematik/Ganzrationale%20Funktionen/Produktform#erkunden]]
18 18  {{/lernende}}
... ... @@ -26,10 +26,16 @@
26 26  |[[image:1-fach.svg||width=100]]| |5-fach |
27 27  {{/aufgabe}}
28 28  
29 -{{aufgabe id="Arithmagon Quadratische Formen" afb="I" kompetenzen="K4" quelle="Martina Wagner" cc="by-sa" zeit="5"}}
33 +{{aufgabe id="Arithmagon Quadratische Formen" afb="I" kompetenzen="K4, K5" quelle="Martina Wagner" cc="by-sa" zeit="5"}}
34 +Ermittle, welche Zahlen in die leeren Kästchen bei den Funktionsgleichungen eingetragen werden müssen.
30 30  [[image:Arithmagon Quadratische Formen.svg||width=500 style=float:left]]
31 31  {{/aufgabe}}
32 32  
38 +{{aufgabe id="Arithmagon Darstellungsformen" afb="III" kompetenzen="K2, K4, K5" tags="problemlösen" quelle="Martina, Dirk, Caroline, Martin" cc="BY-SA" zeit="10"}}
39 +Ermittle, welche Zahlen in die leeren Kästchen bei den Funktionsgleichungen eingetragen werden müssen und beschreibe in den blau hinterlegten Kästchen die Vorgehensweise für die Umwandlung in die andere Funktionsgleichung.
40 +[[image:Arithmagon Polynomfunktion Formen.svg|| width=500]]
41 +{{/aufgabe}}
42 +
33 33  {{aufgabe id="Schaubilder zuordnen Teil 1" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="5"}}
34 34  [[image:Polynome_zuordnen-Grad_drei.svg||width=500 style=float:right]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl.
35 35  (% style="list-style: alphastyle" %)
... ... @@ -81,26 +81,25 @@
81 81  1. {{formula}}f(x)=-\frac{1}{16}\cdot (x-2)^2\cdot (x-8){{/formula}}
82 82  1. {{formula}}f(x)=(x-3)\cdot (x^2+3x+9){{/formula}}
83 83  1. {{formula}}f(x)=3\,x^3-33\,x^2+96\,x-84{{/formula}}
84 -Hinweis: Die Funktion //f// besitzt nur die beiden Nullstellen {{formula}} x_1 =1 {{/formula}} und {{formula}} x_2 =7 {{/formula}}.
94 +Hinweis: Die Funktion //f// besitzt nur die beiden Nullstellen {{formula}} x_1 =2 {{/formula}} und {{formula}} x_2 =7 {{/formula}}.
85 85  1. {{formula}}f(x)=-2\,x^4+18\,x^2+8\,x-24{{/formula}}
86 86  Hinweis: Die Funktion //f// besitzt nur die Nullstellen {{formula}} x_1 =-2, x_2=1 {{/formula}} und {{formula}} x_3 =3 {{/formula}}.
87 87  {{/aufgabe}}
88 88  
89 -{{aufgabe id="Parabelmaschine" afb="II" kompetenzen="K2, K5" tags="problemlösen" quelle="Simon Oswald" cc="BY-SA" cc="by-sa" zeit="20"}}
90 -[[image:Parabelmaschine.PNG||width="240" style="float: right"]]
91 -Denke dir zwei Zahlen, eine positiv, eine negativ.
92 -Wenn du diese Zahlen quadrierst, erhältst du zwei Punkte auf der Normalparabel.
99 +{{aufgabe id="Parabelmaschine" afb="II" kompetenzen="K2, K5" tags="problemlösen" quelle="Simon Oswald" cc="by-sa" zeit="20"}}
100 +[[image:Parabelmaschine.PNG||width="240" style="float: right"]]Denke dir zwei Zahlen, eine positive, eine negative. Wenn du diese Zahlen quadrierst, erhältst du zwei Punkte auf der Normalparabel.
93 93  
94 94  Ermittle, wo die Verbindungslinie dieser zwei Punkte die y-Achse schneidet!
95 95  
96 96  {{lehrende}}
97 -**Variante :** Offene Aufgabe für den Unterricht & für die Klassenarbeit
98 -Wo schneidet die Verbindungslinie dieser zwei Punkte die y-Achse?
105 +**Zusatzfrage:** Und wenn beide Zahlen positiv sind?
99 99  
100 -Und wenn beide Zahlen positiv sind?
107 +**Variante:** Aufgabe für die Klassenarbeit
101 101  
102 -Zur Problemlösung legen dir zwei Mitschüler die Ergebnisse zweier Lösungen vor.
109 +Wo schneidet die Verbindungslinie dieser zwei Punkte die y-Achse?
103 103  
111 +Zur Problemlösung legen dir zwei Mitschüler die Ergebnisse ihrer Lösungen vor.
112 +
104 104  Schüler 1:
105 105  Die Gerade durch die beiden Punkte {{formula}} P(a|a^2){{/formula}} und {{formula}}Q(b|b^2){{/formula}} schneidet die y-Achse bei {{formula}}S(0 | |a\cdot b|){{/formula}}.
106 106  
... ... @@ -121,7 +121,6 @@
121 121  {{/aufgabe}}
122 122  
123 123  {{lehrende}}
124 -[[Polynomfunktionsgraphen begreifen]]
125 125  K3 soll hier nicht bedient werden .. das kommt in BPE 3.5
126 126  {{/lehrende}}
127 127  
Arithmagon Quadratische Formen.svg
Größe
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Inhalt
Arithmagon Polynomfunktion Formen.svg
Author
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1 +XWiki.holgerengels
Größe
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CYLsD2jfO8wNVJ/eJ9n+wLgTk2oPKpgj1g+WqN9IreTk4+LvtCYY3NMs5JCpg+pgucedWK/c0v5s+7hfPNH33rmY+vexwXda817c5+u8O0m007WDpcQoo3wDlQHCCIo/DPLb/y7P1kbAzM/cd0AbZvnOcF6kn3dGwr/aTsC4E5NqDyqYI9YPnMJDq1/xuSdsUJa2yWcU5SwPQxXTj3vO3p231nUCwb6Spcuy3jNIQWbwtu1sA6F3ZM256x/bdxt6+MC4W5/5guwPaN87xAPel9l5adLPtCYI4NqHyqYA9YPvfcVK1d20z2h8Aam2WckxQwfSxXvZE08Z7a93a6lb5dxoQQW7wt/atTBuPDQYSMCYG1/wDTBdi+cZ0XWf8BDN3ibeqL7A+BNTaLyqcK9oDlq7VnFg0mUCt5rewPgTU2y7gmqYXpi3VNnTz1382Eucoe2S5e9ppvTjXTTMaFwireYLo5vfXi07f/RzvWWiu9Yro9/ccyTkPs/nNhugDbN67zYlFrejdbvJNTkoWyPwTW2CwqnyrYA5YPN1EMLumJXPnLwhqbZVyT1ML0xbiyk7I/wncYg2LYSK/58LUffouMi4FZvAHGV2+m1zpjvgKvQ8b5ErP/JEwXYPvGdV6Y9/NoW7xlXyissVlUPlWwB0zfjmfuvKZbvBvZ+bIvBObYwLgmqYXpC3X1L/u8cVAEm+lybA/1FcEu3hgfbhCrt7KzZ8eefT70FB7z9TJdgO0b13lhivdH8T7ucOYut8m+UFhjs6h8qmAPmL43fOiNl/cnzhdlXwjMsYFxTVIL0xfiwg0R9Way1il+g1UBQ3zDGEXxtn8frDHf7N6VtzbkmYfM18t0AbZvXOeFef+6B4N7nrPXp2RfKKyxWVQ+VbAHTN+BHzlomZ00OGcq+7UwxwbGNUktTJ/WlbSThbgFfVD0xBdEWl8ZoyzewBy17Tf4JWRe16JGuqXbX4b0xcB0AbZvHOdFckryp/b9M3WlLftDYYzNReVTBXvA9B3/iRMHDwmtL82ivcyxgXFMUhemT+PCmuzuETeWZ5UxGp8Poy7eoH9Tjz39s0azFnSeLxSmC7B94zgvUD/se3fCZSdHr2liYYzNReVTBXvA9F1787Wvm50s2Xtlvxbm2MA4JqkL0+frwqJR9f7H025rJG+SMcDX58tcFG+A5RqcAn7bdHv6ZTImjyJfCEwXYPvGcV5gETL7vqGuyP5QGGNzUflUwR4wfXD11pzAR9XkXNmvhTk2MI5J6sL0+bi2ai9+kXm/braTZKqVLZExFh+fhrkq3mCqmR1oX6N5vTfhdcsYyTCfFqYLsH3jOC/qzWxlNydNPWH4LEwXUPlUwR4wfXCZon1Wf5LcLPu1MMcGxjFJXZi+MhfWA+ku2Tpb1A6TMS5lPi1zWbxBvZkcMXsEnqxefMzi58sYlzKfBqYLsH3jOC9qs2vYLGf4LEwXUPlUwR4wfd3i3UzeYSdJzHW2gDk2MI5J6sL0lblqjeSi2cKdHCv7JWU+LXNdvIG7JgouQ5P9Lj4+X5guwPaN27zAxQ7O+3RQrM+F6QIqnyrYA6YPrvrSmW0GRzhL021ljAbm2MC4JamE6Rvmsp+O0KaaSUP25zHMF8J8FG9gPo63BvnZSs+U/RZfnw9MF2D7xm1eTLent5vNzzSL9bkwXaDQd/fdd78UnW5bs2bNkXJbTGP64Lri5tW7444otP3OO7D7kSe0MceGhiSV22Iae3xMX5Fr71VLzrPvz25n73Gt7C9qRb7QhuItt8U0zfh2+9Ae19l9sM/KfT8s+7W+ssZ0obF94zYv9j/vgBX2/bn6lqt3i/W5jelCK/LJWt6lsCMQps+6zG/Mv+8d2cR9ackcGxi3IwwJ05fnWu/a52Z2fdEjxfLI88UwX0feoHu+v5neMHsEnrxVxmh8ZTBdgO0bt3lhv6zExQ/4d6zPhekCKp8q2AOmzyney/sTI+pOS+bYwLglqYTpk67+Cm339SZFslb7VBLpi2U+izfAbfO1Vnpnd3800nsXmv3j9mt9w2C6ANs3bvPCvCdf6f1S7Z3WivW5MF1A5VMFe8D0WZd7aZaZJJvKOF+YYwPjlqQSps919Z6A07+E0zSswufG+sAcG5jv4g3wGDW7T7r7xxyR274QXxFMF2D7xmleLDr11f9j8J600v2xLcYnYbqAyqcK9oDps66kmdQHxbuRFj6Etgzm2MA4JWkeTN/A1d7keWYSfGwwIZYmQ59wUwRzbGAcijfAw4ztvukuqGb2F7aH+vJgugDbN07zYqqRDG70s2vSxPgkTBdQ+VTBHjB91oXlYZ0jmqNlnC/MsYFxStI8mD7rmmqkx8weySTLZJwvzLGBcSneAB/PBwcbzaS7GFeMT8J0AbZvnOaFu6iY3RbjkzBdQOVTBXvA9Lku3AjRexOyi90YDcyxgXFK0jyYPrjqp2WvHxSlRnK5jNHAHBsYp+INzEHGlYN91U53jfW5MF2A7RuneWF+kV7ay9f0CrstxidhuoDKpwr2gOlbv3inp/YnQ/AzLZljA+OUpHkwfStWr1hSbyb39N+DNTHfPQDm2MC4FW/sn+5+wv5qpXevvHblBleghBI7NgnbN07zwubsVDM90W6L8UmYLqDyqYI9YPpcFx4Ga49k0na6wI3zhTk2ME5JmgfLh4cSbH/GznfY/V9vz2wjY7SwxmYZt+INsJ/sPsODRWR/KIyxubB94zIvsLql3f9Tjek97fZQXx5MF1D5VMEeMH2uyz48tFs8Ah8eyhwbGJckLYLlwx2U9pF09VZ6uOwPgTU2yzgWb2DXQOnuv1balv0hsMZmYfvGZV7gentbM/BEJ7s91JcH0wVUPlWwB0yfdA2uo21mLXe7L9IXy7gkaREMH5Z0tcWn3kwvsVdPxMIYm8u4Fu/u1Tlmvw0ept0Ov1rKQhtbH7ZvXOYFfll297mpG+72UF8eTBdQ+VTBHjB90lVrJh/p/SbNrne3+yJ9sYxLkhYR68ONN/ZpOIuX7fCN2Ceou8SOTTK2xXuT3sJI252x49f7R4F34dpjGaOBOTbA9o3LvMDyr/19/mF3e6gvD6YLqHyqYA+YPunCAxnsxyD3BghfpC+WcUnSImJ8S65b8l9mr/BJv3H0xz54pIyJIWZseYxz8QYfvOTYwwe5iyt1Ij7BsMfG9o3DvOgvWdA7zdpM1ntyToivCKYLqHyqYA+YPulyvwAKWWFQ+mIZhyQdRoyv3kjeb/c1vqmPceXB9o178YYP+9EpKEfIGF9GMTa5LYZxmBfTzZnX2H0t7wAO8RXBdAGVTxXsAdMnXVj4KCb5pS+WcUjSYYT6ug8Ptvu5lVyHm6RCXUWwfZNQvHs3m2XX232rfYixZRRjk9tiGId54T4sQy6YFuIrgukCKp8q2AOmL89l3oxP94p3eonsKyPPF8M4JOkwQnz9AvP5buK30q/ah+yGuIbB9k1C8cafuMwV+7VXWLLPZ4dl/1XGljGqsbEYh3kxe3NOcrXsC/EVwXQBlU8V7AHTl+eqN7OT+79R78N5Wdk/jDxfDOOQpMMI8dUb2XH2iAULgtntIa5hsH2TUrzBegutNdO/ceN8GOXYGMz3vOh9X9Nb8dK9Ocei9Q2D6QIqnyrYA6Yvz1VrpHs4xaW70Iwveb4Y5jtJy9D66s2ZxCkqF7p9WlcZbN8kFW+A/Wv39aJ2WnP7ypCuWNi++Z4X2J9235qDkdfLfq1vGEwXUPlUwR4wfXmu7uVrgwKTvEP2DyPPF8N8J2kZGh8eoIsnoff37W3yskCNywe2b9KKd9bOXlzv3z6P/Y7TVW7/MKQrFrZvvudFvZG+y9aIhe2t/0z2a33DYLqAyqcK9oDpK3KZN+X2btK30lWybxhFvlDmO0nL0Phqs2vHfGO6MbOz7Ne4fGD7Jq14A/fZivVGcpLsLyLPFQPbN9/zAkvx9vfrF2Qf0PqGwXSBQt8kPsNSbkPb40N7XYU71rZdtv23ZN+wVuQLbUhSuS2mscfn6zv2E8cfap/x94YPvfFy2a9x+Ta2D8Vbbotp7PEV+bC/7b4/7rIT3iv781qRK7SxffM9L1AXsD93X7HnFbIvxDesMV1oRT5Zy7sUdgTC9BW51nt2YmPmVbK/iCJfKPN9hFGGj69/M8MXeh/fsy8X3fzk49LA9k3ikTfA/u7u9/6RIk5fyRhJkSsUtm8+5wUuv7S1YaqVLZH9QOMrg+kCKp8q2AOmr8iFy9cGb5BzRUQZRb5Q5jNJffDx1RrpaYPTJeZjvOy3+Lg0sH2TWryBOH3SlP2SYa4Q2L75nBfmwO6gQW04eetXyH6g8ZXBdAGVTxXsAdM3zGXenNv6R4srZV8Rw3whzGeS+lDmqy/Nth8UjZKn4pS5tLB9k1y8wVQzOd2+F4uWFv8SBWUuLWzffM6LeiNd1a8LX5Z9Fo2vDKYLqHyqYA+YvmEuc8R4Tj/ZvR/OMMwXwnwmqQ/DfK9uv/oPnY/rt2cnZX8kY1yGuUJg+ya9eGP/432whafo9BUoc2lh++ZxXvwO6kHvYCQ7W3ZaFL5SmC6g8qmCPWD6hrnc895YdF325zHMF8I8JqkXw3xmvy23+2+qlbxB9kuGuUJg+ya9eAM8MMC+J6b4FH4S8nFpYPvma17g+y+7/2qNZF/Zb/H1+cB0AZVPFewB0zfMhfNZg+Ljed57mC+E+UpSX4p85iP6ToMi0Uw/KvvzKHKFwvZtDMUb1Jybd7C4kuwHvi5f2L75mhfunavJ0uQvZb/F1+cD0wVUPlWwB0xfmcu8Sbf236z11ustosynZb6S1Jc8X39xry92C3cjvdd3bek8Vwxs38ZSvHETGt6Xfl5/US6qBHxdvrB98zUvZtf7T2+VfS6+Ph+YLqDyqYI9YPrKXM6VEnf5rHNS5tMyX0nqS56v5tyMU2+l+8v+IvJcMbB9G0vxBnhf7Hs06rU5ANs3H/Oiu55J/8EhZU/a8vH5wnQBlU8V7AHTV+YySb67TfJFp5avD1Hm0zIfSapB+rAWjFMUPuH2lSFdsbB9G1PxBnh/uu9VK/36VDvbwu3Tuspg++ZjXiTNpD44KMlZz8TFx+cL0wVUPlWwB0xfmQvrbwzeMPG0jDzKfFrmI0k1SJ/zWKi7au3apm5fGdIVC9u3sRXv7umTZnJP//36jNundZXB9s3HvHCfsoUrqWS/i4/PF6YLqHyqYA+YPh9XrZFe0Sve6c2yT+Lj0zAfSarB9U210qMGR92tmTe7cT6McmwMNrbiDeqNdB/7npniNHgMXYhrGGzffMyL2uD7r+zvZJ/Ex+cL0wVUPlWwB0yfj8sU7cMGCV5yNOnj0zAfSarB+vBkHLOfvtbdR430Uhnnw6jGxmJjLN4A71f/4ORreB+xLdRVBNs31/MC835wYGLqgeyXlPk0MF1A5VMFe8D0+bjWe2SXOVKR/S4+Pg1znaRa4FvvyTjN9D58HJdxPoxibHJbDBtr8e4vgdx9sIB98k6oqwi2b67nBa7ptjXA59FyZT4NTBdQ+VTBHjB9ni7cVdW7Vb5kiVhPnzdznaRa4HOfjIN1jmWML6MYm9wWw8ZavAG+z7HvoSngH4hx5cH2zfW8cC4RvE325VHm08B0AZVPFewB0+frGlwy2Eq/OuyZgL4+X+Y6SbWcennzHbhaoVe4k+s2aW/yPBnjC3tsbN/GXLxxGRzev36Of7115elvlzExxIwtj7mcF5jv9pmgPot6gWE+LUwXUPlUwR4wfb6uWjvddfCxaciiPr4+X+YySUPYcfnO3Se1+H6cHAZ7bGzfxly8gXt6cMczd7ld9scQOzbJXM6L9RdXy3aR/XkM82lhuoDKpwr2gOnzdb2svfPv2y/k8m5qsPj6fJnLJNWCS6ewIH13n7TSo2S/FubYANu3sRdvYI4s34/3E++rz6WxvjDG5jKX86LWyE7pFm4z/1EHZH8ew3xamC6g8qmCPWD6NK56K/1Y/zdw4a2xGp8Pc5mkGrLTspea/XBfr3hn1w87leQLa2wWtu+5ULy7pwjM+9n/pRz85bOEMTaXuZwXmO/9eb/eA7OHMcynhekChb6N5TFoee3Ajxy0zD5OasXqFUtkv9bn05CkcltMY41vl7Nedwv2w/Zn7PTg6ZeffoDsD2mssdnG9qF4y20xjT0+lg/nu/G+4v3d+czX3ST7QxprbLbN1bxYvnr52+ycN/P/NNlf1Ip8IY3pQivyyVrepbAjEKZP45puT7/MnvuabmV7yX6g8fkwl0cYvtSaydvsfnjrqv3Pkf2hMMbmwvY9F468Lfucu9+59j3WrE9TBHNsYK7mRa2RvMnuB82nkCJfCEwXUPlUwR4wfVqXeRM/003oRvpJ2Qe0vjLmKkl9WbR065fYFenqreS6WJ8L0wXYvudS8YbLvMc39HP93vrS+l/IGA3MsYG5mhf1Zvopm+uybxhFvhCYLqDyqYI9YPq0LnMUcrj9TbywvfWfyX6tr4y5SlIv2ps8zy4V0F3MqJlNRfkETBdg+55rxdtdZAzvu9n8OzLOF+bYwFzMCyxlPPj04XFXpUueLxSmC6h8qmAPmD6ty31Aw3Qr3eBaWK2vjLlIUl9qzeQdzmQ+AdtifBKmC7B9z7XijT/rzezkYfnuC3NsYC7mhZvvwx68kEeeLxSmC6h8qmAPmL4QV32wct6GC9SE+IYxF0nqQ61d28zeqGDarXYB/1BfHkwXYPuei8Ub73O9mfSeQ4r33+SBjPWBOTYwF/PCzPMr+0fd18q+MvJ8oTBdQOVTBXvA9IW4phrpofY38panZv/T7QvxDWMuktQH/KKyr9m9SSnUlwfTBdi+52LxBtPt6e0Gn7hyDlh8YI4NjHpe4By/fc0h17tLXwxMF1D5VMEeMH0hroW9a5z7yTzzDrcvxDeMUSepD1PN9J2zibz+E0RCfEUwXYDte64Wb2COuts2B5APbp8P0hfLqOcF1uiZPVjZ+iVunw/SFwPTBVQ+VbAHTF+oCx+lesUsvdLdHuorYtRJWkatUXu5c7rkC4uPWfx8t1/rGwbTBdi+53TxPr72Arz/3TxAPpi8cPvLkL5YRj0vaq3s6u5rbSRXu9t9kb4YmC6g8qmCPWD6Ql3uUzXcq05CfUWMOkmHgqtLbBI38aTx6a1liMpXAtMF2L7ncvEGeP9tLiAvfJ7pasnzxTDKeYEj7ZhPGYD5epkuoPKpgj1g+kJd7qmTeivd224P9RUxyiQtw10mtGg9F42vDKYLsH3P9eINas7DpWut5D2yv4giXyijnBfu04U0N+a4MF8v0wVUPlWwB0xfjMs+gQQL2NttMb48Rpmkw5huTL9yMEmb6d8XLcjj6/OB6QJsX1W8N9kEp83qzfQmmxvIExmTR5EvlFHOC+R796CsmV7ixmhgvl6mC6h8qmAPmL4Y11Rjes9BEvdPKcT48hhlkhaBj8OD0yWt9Ot4araMsfj4fGG6ANtXFe8e7lPUsYiVz+mTYb4QRjUv6u2ZbQavrZHuIeN8Yb5epguofKpgD5i+GBce/1VvJmv7b/ZybIvx5TGqJB1GrZG9b5DAreyDst/Fx+cL0wXYvqp4z+I+Pcl9cHERZT4to5oXtVZyVv91rZExGpivl+kCKp8q2AOmL9aFOw1tEi9ov/oPY32SUSVpEfXmTGJfz1Qz/azsl5T5NDBdgO2rivcsC85f8Hu1/ukFtOn29LSMcSnzaRnFvDCv4Y/t6zEHZcfKGA3M18t0AZVPFewB0xfrStvpgtlilx0Y65OMIknlNgvupqs1k1t6R9zpVxc1sr+SMZJhPi1MF2D7quK9PrXGzKtqjeT+Xv6bvDm+9gIZY/HxaRjFvKgvTQ62cxkXJMgYDczXy3QBlU8V7AHTx3CZBL7cHqkyfC6jSFK5zWI+RZwzOJLyXMdimE8L0wXYvqp4b0itlR0yOFptZWfLfouvz5dRzAu77IWZx5+Q/VqYr5fpAiqfKtgDpo/hctf8PeziI46R/TGMIknlNjDVTHaa/ciYflT2F1HkC4HpAmxfVbzzqTWziwefPpcmO8p+oPH5wJ4Xh150+LGD19CY2VP2a2G+XqYLqHyqYA+YPoard7ohvQ9v/M7LX1v4iLQQ2Ema93pxLasZ+1395P3KVu3FL5IxReT5QmG6ANtXFe98klOSPzV5Yx9EfZdc7wdofD6w5wXmbffApZHeK+8iDoH5epkuoPKpgj1g+lgu3MSCNx+PSyr78kYDO0nl6+1eFthMVg+Outsz27j9ZUhfDEwXYPuq4l3M+pfYJZfj7ly3X+srgzkvaqdmqX2Qtl3qOBbm62W6QKFvY36G5bB28fUX//WrT9/uf+PZf7udtce1sj+0IUnltpgmX+/eK5estM/oe/O5b71Axpc16YtpTBca24fiLbfFNPb4mL4Q1xv/9i0X2lxasmr/c2J9wxpzXuz2oT2uw7zF/L3kM5fsJftDGvP1Ml1oRT5Zy7sUdgTC9DFdWHHP/gbXLt5eBPMIA7iv1xwh7Ts4Wmqmn3bjfGHuP6YLsH3Vkfdwuvc9tJLrBp/iGuk+ti/ENwzWvOguvNb/xFxvJE3ZHwrz9TJdQOVTBXvA9DFdKNiDj1/N9FTZHwIrSS329dbb22w+KNyt9O4s8NIo5v5jugDbVxXvcqbaW7+i3kzuGRTwU+qbY3uorwjWvLBL3WLexl4e6MJ8vUwXUPlUwR4wfUwX2P3sPbvnj+vNdM2rTnzNC2W/FlaSWvB6Ma7116eY2VnG+cLcf0wXYPuq4u1HrZHu6nyiuxHXf8f48mDMC9xUZ8Z3B8a5+4o98YxOGszXy3QBlU8V7AHTx3SBM69asb+TuNFH34wkdcHrrbeyZbNH3f4rw+XB3H9MF2D7quLtz1QzPWw2x9J2rE/CmBfml8xSO8YVq1cskf0xMF8v0wVUPlWwB0wf0wXgQ9G2SYE7MGWMBkaSuuy9at9VzqQ6R/ZrYe4/pguwfVXx1mFy7G9truGLcdkfQ+y8wOmcwTxoZKcwXq8L08d0AZVPFewB08d0AfhwnfRsYqSXyhgNsUnqYo6y32rPyeMJQEXLvGpg7j+mC7B9VfHW0V0+tpFehXzrXkLbyN4iY0KJnRe4i7I3D5J7MF8Zr9eF6WO6gMqnCvaA6WO6gPWZpDjCFvB6K9tFxvkSm6SW6ebMa0zB/lq/eH8la2cvljEhMPcf0wXYvqp460GeId+6V3OY/NPeR1BEzLyYaiSvs3MTp3ewjfV6LUwf0wVUPlWwB0wf0wWsD3dd1pvZl7tJ0krv1Ny16BKTpJZ6s76VGUf3DjJMouSUZKGMCYW5/5guwPZVxTuMqWY25VyFdSvyUcZoCZ0XW5yyzZ/U+ncTm18mX8LqiNjOfL2A6WO6gMqnCvaA6WO6gOvDx8TB0bdivRCX0CS19J+I0/1GHe29Fx52nIyJgbn/mC7A9lXFO5x3X3DYYOlkrIE/X98Fmf//QjsOc1D1Rrud/XqZPqYLqHyqYA+YPqYLSJ9JkPNmkyU5wO3zITRJQf8GBLvmRPdZm3J8sTB9TBdg+6riHQ58yL/BXGimX4m5rjpkXpgDqIMG/39j/S/rR/F65bZQmC6g8qmCPWD6mC4gfbimutY/ZYHms0a2S0iSAhxxY4la+/9irXFsl+OLheljugDbVxXvcKwPSw3P5mT62dAjcO28WO+mtGZyy8L2wj9w+0f1ehkwXUDlUwV7wPQxXSDPh4VvnIT9BM6Hy5gitEkKakvTbWuzqwTiUWaH2L688cXA9DFdgO2rinc4rq/eTN49W0jTuxYtTWbcWB8086L7/VMj/aT9P/OeyTrK1xsL0wVUPlWwB0wf0wWKfOYj29GzxTS91H5RUoYmSYG7Lne3NZJ93f6i8YXC9DFdgO2rinc40mfmw37r5Wkz3cHtL8N3XnQf19bILpv9f/KftynHFwvTx3QBlU8V7AHTx3SBYT530fp6Kztf9ufhm6RgqpEe406I6Va2l4wZNr4QmD6mC7B9VfEOJ8/nPsSkX1g/IGOK8J0X5v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Arithmagon Quadratische Formen Lösung.svg
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