Question

1)Sa se determine functiile de gradul 2 f:R->R,stiind ca:
a)f(0)=1;f(1)=3;f(2)=7
b)f(-1)=1;f(2)=7;f(-2)=3

Answer 1

a. f(x)=ax²+bx+c
f(0)=1, c=1
f(1)=3, a+b+1=3, a+b=2
f(2)=7, 4a+2b+1=7, 4a+2b=6, 2a+b=3, a+a+b=3, a+2=3, a=1, b=2-a=1
f(x)=x²+2x+1

b. f(-1)=a-b+c=1
f(2)=4a+2b+c=7
f(-2)=4a-2b+c=3
adunam ultimele doua relatii
8a+2c=10
4a+c=5, c=5-4a
inlocuim in primele doua
a-b+5-4a=1, -3a-b=-4
4a+2b+5-4a=7, 2b=2, b=1
-3a-1=-4, -3a=-3, a=1
c=5-4a=1
f(x)=x²+x+1