Question

已知函数f(x)是二次函数,且满足f(x+1)+f(x-1)=2x2+4x+5,则f(x)=_____ 要具体过程,谢

Answer 1

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

f(x+1)+f(x-1)=a(x+1)^2+b(x+1)+c+a(x-1)^2+b(x-1)+c

=2ax^2+2bx+2(a+c)=2x^2+4x+5

2a=2

2b=4

2(a+c)=5

a=1

b=2

c=3/2

所以：f(x)=x^2+2x+(3/2)