已知：如圖14，拋物線與軸交於點，點，與直線相交於點，點，直線與軸交於點．（1）寫出直線的解析式．（2）求的面...
問題詳情：
已知：如圖14，拋物線
與
軸交於點
，點
，與直線
相交於點
，點
，直線與
軸交於點
．
（1）寫出直線
的解析式．
（2）求
的面積．
（3）若點
在線段
上以每秒1個單位長度的速度從
向
運動（不與
重合），同時，點
在*線上以每秒2個單位長度的速度從向運動．設運動時間為
秒，請寫出
的面積
與的函數關係式，並求出點
運動多少時間時，
的面積最大，最大面積是多少？
【回答】
解：（1）在
中，令
，
，
··············································· 1分
又
點
在
上
的解析式為
·············································································· 2分
（2）由
，得
···················································· 4分
，
，
······························································································· 5分
························································································· 6分
（3）過點
作
於點
······························································································· 7分
·········································································································· 8分
由直線
可得：
在
中，
，
，則
，
······················································································· 9分
···················································································· 10分
····························································································· 11分
此拋物線開口向下，
當
時，
當點
運動2秒時，
的面積達到最大，最大為
．···························· 12分
知識點：相似三角形
題型：綜合題
