Question

已知一元二次函数Y=F(X)满足F(X+1)-F(X)=2X,F(0)=1,

Answer 1

F(X)=ax^2+bx+c

F(0)=1

c=1

F(X)=ax^2+bx+1

F(X+1)=a(x+1)^2+b(x+1)+1=ax^2+2ax+a+bx+b+1

F(X+1)-F(X)

=ax^2+2ax+a+bx+b+1-(ax^2+bx+1)

=2ax+a+b

=2X

2a=2

a=1

a+b=0

b=-1

F(X)=x^2-x+1