Question

f（x）=ax^2+bx+c,a不等于0,对一切x∈【0,1】时,恒有|f(x)|

Answer 1

c=f(0),a+b+c=f(1),a/4+b/2+c=f(0.5）； a+b=f(1)-f(0),& 0.5a+b=2f(0.5)-2f(0) ;

0.5a=f(1)-2f(0.5)+f(0),a=2f(1)-4f(0.5)+2f(0)