The symmetry axis is x=- 1/2, which is called function f 1(x).
When x
1) when a >; When 1/2 and f 1(x) are increasing function, f2(x) takes the minimum value at the symmetry axis x= 1/2, and f2( 1/2)=a-5/4.
At this time, the minimum value of the function f(x) is f2( 1/2), that is, fmin=a-5/4.
2) When
At this time, the minimum value of the function f(x) is f 1(- 1/2), that is, fmin=-(a+5/4).
3) when-1/2≤a≤ 1/2, f 1(x) is increasing function, f2(x) is a decreasing function, and f(x) takes the minimum value at x=a, and fmin = a 2-/kloc-0.
Therefore, the minimum value of f(x): fmin=-(a+5/4), a.
Fmin = a 2- 1,- 1/2≤a≤ 1/2