Lösungen:

 

  1. a) Scheitel: (1|1)                                             
        Scheitelpunktform: y = (x-1)˛ +1
    b) Scheitel: (-2|-1)
        Scheitelpunktform: y = (x+2)˛ -1
    c) Scheitel: (2|0)
        Scheitelpunktform: y = 2(x-2)˛

 

  1. a) x1= -4; x2= 2
    b) x1= 1; x2 = -3
    c) S(1|1)
    d) S(-3|0)

 



  1. a) f(x) = -2x2 – 8x – 6
        LFF: x1/2 =      ā x1 = -3; x2 = -1
        LFF: y = -2(x+3)(x+1)

        SF: xs =  = -2;   ys = 2  S(-2|2)

SF: y = -2(x+2)˛ +2


b) g(x) = x2 -7x +
    LFF: x1/2 =  ā x1 = 5,5; x2 = 1,5
    LFF: y = (x-5,5)(x-1,5)

    SF: xs =  = 3,5;   ys = -4  S(3,5|-4)

    SF: y = (x-3,5)˛ -4

 

 

c) h(x) = -x2 +x

    LFF: x1/2 =  ā x1 = 0; x2 = 6
    LFF: y = -x (x-6)

    SF: xs = – = 3;   ys = 1  S(3|1)

    SF: y = - (x-3)˛ +1

 

 

  1. P(2|10) ; x1=1 ; X2=-3
    y = a(x-1)(x+3)

    P einsetzen:
    10 = a(2-1)(2+3)
    10 = 5a     ā a = 2 ā y = 2(x-1)(x+3)

 

 

  1. S(|1); y = a(x-xs)˛ + ys
    ā y = (x - )˛ +1
    y =  x˛ - x +

 

 

  1. a) 3
    b) 2
    c) 1