Question

已知：如圖14，拋物線與軸交于點(diǎn)，點(diǎn)，與直線相交于點(diǎn)，點(diǎn)，直線與軸交于點(diǎn)．

（1）寫出直線的解析式．

（2）求的面積．

（3）若點(diǎn)在線段上以每秒1個單位長度的速度從向運(yùn)動（不與重合），同時，點(diǎn)在射線上以每秒2個單位長度的速度從向運(yùn)動．設(shè)運(yùn)動時間為秒，請寫出的面積與的函數(shù)關(guān)系式，并求出點(diǎn)運(yùn)動多少時間時，的面積最大，最大面積是多少？

Answer 1

解：（1）在中，令

，

，··············································· 1分

又點(diǎn)在上

的解析式為·············································································· 2分

（2）由，得  ···················································· 4分

，

，······························································································· 5分

························································································· 6分

（3）過點(diǎn)作于點(diǎn)

······························································································· 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(dāng)時，

當(dāng)點(diǎn)運(yùn)動2秒時，的面積達(dá)到最大，最大為．···························· 12分