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(gè)單位長(zhǎng)度的速度從向運(yùn)動(dòng)（不與重合），同時(shí)，點(diǎn)在射線上以每秒2個(gè)單位長(zhǎng)度的速度從向運(yùn)動(dòng)．設(shè)運(yùn)動(dòng)時(shí)間為秒，請(qǐng)寫出的面積與的函數(shù)關(guān)系式，并求出點(diǎn)運(yùn)動(dòng)多少時(shí)間時(shí)，的面積最大，最大面積是多少？

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(shí)，

當(dāng)點(diǎn)運(yùn)動(dòng)2秒時(shí)，的面積達(dá)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(diǎn)，與y軸交于點(diǎn)D(0，8)，直線DC平行于x軸，交拋物線于另一點(diǎn)C．動(dòng)點(diǎn)P以每秒2個(gè)單位長(zhǎng)度的速度從點(diǎn)C出發(fā)，沿C→D運(yùn)動(dòng)．同時(shí)、點(diǎn)Q以每秒1個(gè)單位長(zhǎng)度的速度從點(diǎn)A出發(fā)，沿A→B運(yùn)動(dòng)．連結(jié)PQ、CB．設(shè)點(diǎn)P的運(yùn)動(dòng)時(shí)間為t秒．

(1)求a的值；

(2)當(dāng)t為何值時(shí)，PQ平行于y軸；

(3)當(dāng)四邊形PQBC的面積等于14時(shí)，求t的值．

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