Bestimme die Schnittpunkte rechnerisch:

Question

Aufgabe:

Bestimme die Schnittpunkte rechnerisch:

P1 (x) = -1/4x2+x+3

P2 (x) = 1/2x+1

Answer 1

Hallo,

P1 (x) = -1/4x2+x+3

P2 (x) = 1/2x+1

P1(x)=P2(x)

(-1/4) x^2 +x+3= (1/2 )x +1 |-(1/2 )x -1

(-1/4) x^2 +x/2 +2=0 | *(-4)

x^2 -2x -8=0

x1,2= 1±√(1+8)

x1,2= 1±3

x1=4

x2=-2

in z.B .P2 (x) = 1/2x+1 eingesetzt

y1(4)=3

y2(-2)=0

P1(4/3)

P2(-2/0)

Answer 2

P_1 (x) = -1/4x^2+x+3
P_2 (x) = 1/2x+1

-1/4x^2+x+3= 1/2x+1

-1/4x^2+x-1/2x= -2

-1/4x^2+1/2x= -2|*(-4)

x^2-2x=8

(x-1)^2=8+1=9|\( \sqrt{~~} \)

1.) x-1=3     x₁=4       P_2 (4) = 1/2*4+1=3

2.) x-1=-3    x₂=-2       P_2 (-2) = 1/2*(-2)+1=0