S ( 3 | 2.8 )
N ( 0 | 0 )
N ( 6 | 0 )
f ( x ) = a * x^2 + b * x + c
f ( 0 ) = a
a * 0^2 + b * 0 + c = 0 => c = 0
f ( x ) = a * x^2 + b * x
f ( 6 ) = a * 6^2 + b * 6 = 0
36 * a + 6 * b = 0
Für den Scheitelpunkt
f ( 3 ) = a * 3^2 + 3 * b = 2.8
9a + 3 * b = 2.8
36a + 6 * b = 0
9a + 3 * b = 2.8 | * 2
36a + 6 * b = 0
18a + 6 * b = 5.6 | abziehen
----------------------
18a = -5.6
a = - 14 / 45
Einsetzen
9a + 3b = 2.8
9 * ( -14 /45 ) + 3b = 2.8
b = 1.867
f ( x ) = -14/45 * x ^2 + 1.867 * x