问题
填空题
已知点A(x1,y1)、B(x2,y2)均在抛物线y=ax2+2ax+4(0<a<3)上,若x1<x2,x1+x2=1-a,则y1______y2.(选填“>”“<”或“=”)
答案
将x1代入抛物线,得y1=ax12+2ax1+4,将x2代入抛物线,得y2=ax22+2ax2+4,
y1-y2=a(x12-x22)+2a(x1-x2)
=a(x1-x2)(x1+x2)+2a(x1-x2)
=a(x1-x2)(x1+x2+2)
∵x1+x2=1-a,
∴y1-y2=a(x1-x2)(3-a),
∵0<a<3,x1<x2,
∴y1-y2<0,即y1<y2.
故答案为:<.