题目内容
已知：如图14，抛物线
与
轴交于点
，点
，与直线
相交于点，点
，直线与
轴交于点
．
（1）写出直线
的解析式．
（2）求
的面积．
（3）若点
在线段
上以每秒1个单位长度的速度从向运动（不与
重合），同时，点
在射线上以每秒2个单位长度的速度从向运动．设运动时间为
秒，请写出
的面积
与的函数关系式，并求出点运动多少时间时，的面积最大，最大面积是多少？
解：（1）在中，令
，
，
··············································· 1分
又
点在上
的解析式为
·············································································· 2分
（2）由
，得
···················································· 4分
，
，
······························································································· 5分
························································································· 6分
（3）过点作
于点
······························································································· 7分
·········································································································· 8分
由直线可得：
在
中，
，
，则
，
······················································································· 9分
···················································································· 10分
····························································································· 11分
此抛物线开口向下，当
时，
当点运动2秒时，的面积达到最大，最大为
．···························· 12分
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