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