设二次函数f（x）=ax2+bx+c(a≠O)中,有∣f(0)∣≤1,∣f(1)∣≤1,∣f(-1)∣≤1.求证：对于任意的x∈【-1,1】,有∣f(x)∣≤5/4.在∣f(1)∣≤1和∣f(0)∣≤1条件下-b/2a=1/2时取得f(x)最值,a=-b有什么证据吗

　　设二次函数f（x）=ax2+bx+c(a≠O)中,

　　有∣f(0)∣≤1,∣f(1)∣≤1,∣f(-1)∣≤1.求证：对于任意的x∈【-1,1】,有∣f(x)∣≤5/4.

　　在∣f(1)∣≤1和∣f(0)∣≤1条件下

　　-b/2a=1/2时取得f(x)最值,a=-b

　　有什么证据吗？