已知：如圖14，拋物線與軸交于點，點，與直線相交于點，點，直線與軸交于點．

（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，點在射線上以每秒2個單位長度的速度從向運動．設(shè)運動時間為秒，請寫出的面積與的函數(shù)關(guān)系式，并求出點運動多少時間時，的面積最大，最大面積是多少？

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）過點作于點

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

當(dāng)點運動2秒時，的面積達到最大，最大為．···························· 12分

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科目：初中數(shù)學(xué) 來源：中考必備’04全國中考試題集錦·數(shù)學(xué) 題型：044

如圖，已知拋物y＝x2－ax＋a＋2與x軸交于A、B兩點，與y軸交于點D(0，8)，直線DC平行于x軸，交拋物線于另一點C．動點P以每秒2個單位長度的速度從點C出發(fā)，沿C→D運動．同時、點Q以每秒1個單位長度的速度從點A出發(fā)，沿A→B運動．連結(jié)PQ、CB．設(shè)點P的運動時間為t秒．

(1)求a的值；

(2)當(dāng)t為何值時，PQ平行于y軸；

(3)當(dāng)四邊形PQBC的面積等于14時，求t的值．

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