摘要： 已知点A(a.).B(2a.y).C(3a.y)都在抛物线上. (1)求抛物线与x轴的交点坐标, (2)当a=1时.求△ABC的面积, (3)是否存在含有.y.y.且与a无关的等式?如果存在.试给出一个.并加以证明,如果不存在.说明理由. 解:(1)由5=0.·············································································· 得.．·················································································· ∴抛物线与x轴的交点坐标为(0.0).(.0)．······································· (2)当a=1时.得A.B.C.······························ 分别过点A.B.C作x轴的垂线.垂足分别为D.E.F.则有 =S - - ···················································· =--···································· =5········································································ (3)如:． ········································································· 事实上. =45a2+36a． 3()=3[5×(2a)2+12×2a-(5a2+12a)] =45a2+36a．············ ∴． ····················································································

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