f(x)=x^2+2(1-2a)x+6,
对称轴方程X=-(1-2a),抛物线开口向上,则有
-1≤-(1-2a),
a≥0.
f(2a-1)=(2a-1)^2+2(1-2a)(2a-1)+6
=-(2a-1)^2+6.
1)当a=1/2时,f(2a-1)=6,f(0)=6.此时,
f(2a-1)=f(0)=6.
2)当a≥0且,a≠1/2时,
f(2a-1)-f(0)=-(2a-1)^2
f(x)=x^2+2(1-2a)x+6,
对称轴方程X=-(1-2a),抛物线开口向上,则有
-1≤-(1-2a),
a≥0.
f(2a-1)=(2a-1)^2+2(1-2a)(2a-1)+6
=-(2a-1)^2+6.
1)当a=1/2时,f(2a-1)=6,f(0)=6.此时,
f(2a-1)=f(0)=6.
2)当a≥0且,a≠1/2时,
f(2a-1)-f(0)=-(2a-1)^2