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Zuletzt geändert von Simone Hochrein am 2025/10/01 13:30
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1 (%class=abc%)
2 1. (((Mit den Nullstellen {{formula}}x_1=-3{{/formula}} und {{formula}}x_2=2{{/formula}}:
3
4 {{formula}}
5 \begin{aligned}
6 &f(x) &= a \cdot (x + 3) (x - 2) ~~~(1)
7 \end{aligned}
8 {{/formula}}
9
10 Mit {{formula}}P(0|3){{/formula}}:
11
12 {{formula}}
13 \begin{aligned}
14 &f(0) &= -3 ~~~(2)
15 \end{aligned}
16 {{/formula}}
17
18 {{formula}}(2){{/formula}} in {{formula}}(1){{/formula}}:
19
20 {{formula}}
21 \begin{aligned}
22 a \cdot (0 + 3) (0 - 2) &= -3\\
23 -6a &= -3 \\
24 ~a &= 0,5 \\
25 \end{aligned}
26 {{/formula}}
27
28 {{formula}}
29 \Rightarrow f(x)=0,5\cdot (x+3)(x-2)
30 {{/formula}}
31
32 )))
33 1. (((Mit {{formula}}S(2|4){{/formula}} und {{formula}}a=-2{{/formula}}:
34
35 {{formula}}
36 \Rightarrow f(x)=-2\cdot (x-2)^2+4
37 {{/formula}}
38
39 )))
40 1. (((Mit {{formula}}S(3|1){{/formula}}:
41
42 {{formula}}
43 f(x) = a \cdot (x-3)^2+1
44 {{/formula}}
45
46 Mit {{formula}}A(5|2){{/formula}}:
47
48 {{formula}}
49 \begin{aligned}
50 a \cdot (5-3)^2+1&=2 \\
51 a \cdot 4+1&=2 \\
52 4a&=1 \\
53 a&=0,25
54 \end{aligned}{{/formula}}
55 )))