一、案例分析题目:已知二次函数f(x)=ax~2+bx+c的图像过点(-1,0),问是否存在常数a,b,c,使不等式x≤f(x)≤1/2(1+x~2)对一切x∈R都成立?此题不仅在辅导资料上流传甚广,而且它有一种奇妙的解法也比较流行,那就是:对于不等式x≤f(x)≤1/2(1+x~2),令x=1,得到1≤f(1)≤1,从而知f(1)=1,即a+b+c=1①;然后根据二次函数f(x)=ax~2+bx+c的图像过点(-1,0),知a-b+c=0②,由①、②知b=1/2,a+c= First, the case analysis of the problem: known quadratic function f (x) = ax ~ 2 + bx + c image over point (-1,0), asked whether there is a constant b, c, so inequality x ≤ f x) ≤1 / 2 (1 + x ~ 2) for all x∈R? This question not only spreads widely in the guidance material, but also has a fantastic solution is also more popular, that is: for the inequality x ≤ Let f (1) = 1, that is, a + b + c = 1 ①, then let f (x) ≤ 1/2 (1 + x ~ 2) From the point (-1, 0) of the quadratic function f (x) = ax ~ 2 + bx + c, we know that a-b + c = =