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Version 3.1 von Simone Hochrein am 2025/10/01 12:13
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1 Mit den Nullstellen {{formula}}x_1=-3{{/formula}} und {{formula}}x_2=2{{/formula}}:
2
3 {{formula}}
4 \begin{aligned}
5 &f(x) &= a \cdot (x + 3) \cdot (x - 2) ~~~(1)
6 \end{aligned}
7 {{/formula}}
8
9 Mit {{formula}}P(0|3){{/formula}}:
10
11 {{formula}}
12 \begin{aligned}
13 &f(0) &= -3 ~~~(2)
14 \end{aligned}
15 {{/formula}}
16
17 {{formula}}(2){{/formula}} in {{formula}}(1){{/formula}}:
18
19 {{formula}}
20 \begin{aligned}
21 a \cdot (0 + 3) \cdot (0 - 2) &= -3\\
22 -6a &= -3 \\
23 ~a &= 0,5 \\
24 \end{aligned}
25 {{/formula}}