Question

Determinati coordonatele varfului parabolei asociate functiei f:R->R f(x)= x la puterea a 2 - 2x

Answer 1

V(-b/2a;-Δ/4a);
x²-2x este o ecuatie de gradul doi forma incompleta,si anume a≠0,b≠0,c=0;
x²-2x+0=0
Δ=(-2)²-4*1*0=4-0=4>0
x1=2+√4/2=2+2/2=4/2=2       A(2:0);B(0;0)
x2=2-√4/2=2-2/2=0/2=0.
-b/2a=2/2*1=2/2=1(x);
-Δ/4a=-4/4=-1(y).
Deci:
V(1;-1).
Sau se poate si asa:
stiind ca -b/2a=1 putem afla cealalta coordonata adica -Δ/4a.
Adica:
V(1;x)
f(1)=x⇒1²-2*1=x⇒x=1-2⇒x=-1;
Bafta!