Question

Determinati functia de gradul al doilea f:R-R, stiind ca verfica conditiile f(0)=1 f(1)=3 f(2)=7

Answer 1

Fie f(x)=ax^2 + bx +c

Ea verifica

a*0 + b*0 +c =1

c=1

a+b+c=3

a+b=3-1=2, deci b=2-a

4a+2b+1=7

4a+2b=6 l :2

2a+b=3 si-l inlocuiesc pe b=2-a

2a+2-a =3

a=3-2=1

b=2-1=1

Deci avem f(x) = x^2 + x +1

Verific: 0+0+1=1

1+1+1=3

4+2+1=7, corect.