Odpowiedzi

2009-12-15T20:47:30+01:00
A)
x1 = 3, y1 = 5, P =(6;8)
y = a(x-x1)(x-x2)
y =a(x -3)(x-5)
8 = a(6-3)(6-5) = 3*1*a = 3a
a = 8/3
Odp. y =(8/3)(x-3)(x -5) lub
y = (8/3)(x² -8x + 15) = (8/3)x² -(64/3)x +40
b)
x1 =-1, x2 = 4, P =(3,9)
y = a(x +1)(x-4)
9 = a(3+1)(3-4) = -4a
a = - 9/4
y =( -9/4)(x +1)(x -4) lub
y = (-9/4)(x²-3x -4) = (-9/4)x² +(27/4)x +9
c)
x1 = 2, x2 = -6, P = (-3;5)
y = a(x-2)(x +6)
5 = a(-3-2)(-3 +6) = (-5)*3a = -15a
a = -5/15 = -1/3
y =(-1/3)(x-2)(x+6) lub
y = (-1/3)(x² +4x -12) = (-1/3)x² -(4/3)x + 4