1、拋物線開口向上,對稱軸為x=-a/2
當(dāng)-a/2<-1即a>2時ymin=f(-1)=4-a=-3,所以a=7
當(dāng)-1<=-a/2<=1即-2<=a<=2時,ymin=f(-a/2)=a^2/4-a^2/2+3=3-a^2/4=-3
所以a=±2√6不∈[-2,2],舍去
當(dāng)-a/2>1即a<-2時,ymin=1=4+a=-3,a=-7
綜上,a=-7或a=7
2、(1)f(x)關(guān)于x=-3/2對稱,所以-b/2a=-3/2即b=3a
f(1)=0所以a+b=2/3,解得a=1/6,b=1/2,f(x)=x^2/6+x/2-2/3
(2)a1=S1=f(a1)=a1^2/6+a1/2-2/3,解得a1=4(a1=-1舍去）
an=Sn-S(n-1)=f(an)-f(an-1)=an^2/6+an/2-[a(n-1)]^2/6-a(n-1)/2
整理得(an+a(n-1))(an-a(n-1)-3)=0
因為{an}是正項數(shù)列,所以an+a(n-1)>0,故有an-a(n-1)=3
所以｛an}是首項為4,公差為3的等差數(shù)列,故an=4+3(n-1)=3n+1
（3）bn=(3n+1)/2^n
Tn=4/2+7/2^2+……+(3n-2)/2^(n-1)+(3n+1)/2^n
(1/2)Tn=4/2^2+7/2^3……+(3n-2)/2^n+(3n+1)/2^(n+1)
相減得(1/2)Tn=2+3(1/2^2+1/2^3+……+1/2^n)-(3n+1)/2^(n+1)
=2+3(1/2-1/2^n)-(3n+1)/2^(n+1)
=(7/2)-(3n+7)/2^(n+1)
Tn=7-(3n+7)/2^n