①∵抛物线y2=(x-3)2+1开口向上,顶点坐标在x轴的上方, ∴无论x取何值,y2的值总是正数,故本小题正确; ②把A(1,3)代入,抛物线y1=a(x+2)2-3得,3=a(1+2)2-3,解得a=,故本小题错误; ③由两函数图象可知,抛物线y1=a(x+2)2-3解析式为y1=(x+2)2-3,当x=0时,y1=(0+2)2-3=-,y2=(0-3)2+1=,故y2-y1=+=,故本小题错误; ④∵物线y1=a(x+2)2-3与y2=(x-3)2+1交于点A(1,3), ∴y1的对称轴为x=-2,y2的对称轴为x=3, ∴B(-5,3),C(5,3) ∴AB=6,AC=4, ∴2AB=3AC,故本小题正确. 故答案为:①④. |