∵y=f(x)=-
(x−)2+
(a
2-a+2),对称轴为x=
,…1
(1)当0≤
≤1时,即0≤a≤2时,f(x)max=
(a
2-a+2),
由
(a
2-a+2)=2得a=-2或a=3与0≤a≤2矛盾,不和要求…5
(2)当
<0,即a<0时,f(x)在[0,1]上单调递减,f(x)max=f(0),由f(0)=2
得-
+
=2,解得a=-6…9
(3)当
>1,即a>2时,f(x)在[0,1]上单调递增,f(x)max=f(1),
由f(1)=2得:-1+a-
+
=2,解得a=
…13
综上所述,a=-6或a=
…14