Hi. Hier findest du eine Zusammenfassung der Themen: p-q-Formle, ausklammern, quadratische Ergänzung, quadratische und lineare Funktionen/Gleichungen mit vielen Beispielen und Rechnungen.
& G:n-usklammern aka Faktorisieren kann man nur bei
folgender Form der Gleichung:ax" bx
= 0
=
& G:Umformen und Wurzel ziehen kann man nur b
3 S) :
ex2 -
27 0
=
27
+
3 S
2. x. X
.
2x2 6x
+
0
= T 5x2 x
=
-
x
3x
2
27
=
:3
Wurzel istd i e
2
Umkehrung von
x.12x 6) +
0
=
5x2 -
1x 0 = T x
2
9
=
8
-
X1 2x 6 0
=
6 4 15x 1) 0 3
x1 3
-
oder
+
·X2 =
-
=
= -
=
2x =
- 6 :2 x
05x
= -
1 0 =
1
+
2.
Lösung nicht
vergessen
x
2
=
- 3 5x 1
= :5
x 0,2
=
oder I
3 UC SO 6U6 UC SO. C
Errechnung der
quadratischen Ergänzung (9. E.): quadratischen Ergänzung (9. E.)
14:212 4
=
typisch quadratisch:x
+
6x 8
+
Übung:Qua
3 S) :
x +
4x 5
=
typisch linear: xoder 5x-7
y
=
D 6: SOC keins von beiden:
y 1
=
oder
y
x3
=
7
+
=
(a b) Beispiel(1):(x 212
2
+ a 2ab
+
b2
+
+
x
=
4x 4
+ +
(a b).(a b) a b2 +
+ + =
ab
+
ab
+ +
(x 2).(x 2)
+ +
x
=
2x 2x 4 +
+
=a
+
2ab b2
+ x2 4x
=
+
4
+
C C
C
C .
I- q 3 S :x 2
+
1 -
6x) 8 +
0
=
x
=
-
2 =(2 -
q
3 S -Rechnung einer quadratischen Gleichung m
11- 8
-
6 -
p x +
=
=
-
2
13
+ 2
4
eine
typische gadratische Gleichung:a x bx c 8 3 8 x 4x 5
9. E. 4 2x 12
+ = +
X
9
+
= = - = -
2 2
9
2
x (
+ -
6x) 8 +
0
=
x 3
=
= -
8 x 4x 4
+ +
5 4
=
+
bin. F x -
6
x2 px q
+ +
0
=
x 3
=
1
= (x 2 =9
+
x 3 1
= +
4
=
oder x 3
=
-
1 2
=
x 2 +
3
=
p
x 2 3-2 oder x + 2 3-2
=
+ = -
2
x 1 x 5 x 6
= =
-
-
&6 .
und optional wie man eine quadratische x
2
px
+
q
+
0
= -
9 x2 -
6x
und Gleichung in eine
p-a-Formel um - x2 px + =
-
q +Ip2 oder
( ({ 5;13 -
x
2
-
6x
+
(P (2 3
-
und rechnen kann:x px
+
=
-
9 I (x -
und x 2 (24
+
=
-
9 x 3
+
x -
3 5 =
3
+
3 S) :
mitder
p-g-Formel. x2 +
5x 4
+
0
=
x
2
+
19
= oder x
2
+ =
-
19 - x 8
=
5
p
=
9 4
=
x -
=
I (*9 +
oder x -
=
2 -
129 (
X =
-2I2 -
q
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