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26．如圖16.在平面直角坐標(biāo)系中.直線與軸交于點.與軸交于點.拋物線經(jīng)過三點． (1)求過三點拋物線的解析式并求出頂點的坐標(biāo), (2)在拋物線上是否存在點.使為直角三角形.若存在.直接寫出點坐標(biāo),若不存在.請說明理由, (3)試探究在直線上是否存在一點.使得的周長最小.若存在.求出點的坐標(biāo),若不存在.請說明理由． 解:(1)直線與軸交于點.與軸交于點． .························································································· 1分 點都在拋物線上. 拋物線的解析式為························································ 3分 頂點······························································································· 4分 (2)存在··············································································································· 5分 ············································································································· 7分 ············································································································ 9分 (3)存在·············································································································· 10分 理由: 解法一: 延長到點.使.連接交直線于點.則點就是所求的點． ····················································································· 11分 過點作于點． 點在拋物線上. 在中.. .. 在中.. ..··············································· 12分 設(shè)直線的解析式為 解得 ································································································ 13分 解得 在直線上存在點.使得的周長最小.此時．··· 14分 解法二: 過點作的垂線交軸于點.則點為點關(guān)于直線的對稱點．連接交于點.則點即為所求．················································································ 11分 過點作軸于點.則.． . 同方法一可求得． 在中...可求得. 為線段的垂直平分線.可證得為等邊三角形. 垂直平分． 即點為點關(guān)于的對稱點．············································· 12分 設(shè)直線的解析式為.由題意得 解得 ································································································ 13分 解得 在直線上存在點.使得的周長最小.此時．··· 14分 【查看更多】

 

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計算：
（1）(
12
+
18
)×2
6

（2）(4
15
-3
5
)÷2
5

（3）(2
5
+3)(2
5
-2)
（4）(
6
+
3
)2
（5）(2
6
-3
2
)2
（6）(3
3
+2
2
)(3
3
-2
2
)．

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列方程或方程組解應(yīng)用題：
世界上最長最快的高速鐵路武廣高速于2009年12月26日開通運營，預(yù)計高速列車在武漢、廣州間單程直達運行時間為3小時．某次試車時，試驗列車由武漢到廣州的行駛時間比預(yù)計時間多用了36分鐘，由廣州返回武漢的行駛時間與預(yù)計時間相同．如果這次試車時，由廣州返回武漢比去廣州時平均每分鐘多行駛1千米，那么這次試車時由武漢到廣州的平均速度是每小時多少千米？

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2008年12月26日，中國海軍艦艇編隊起航赴索馬里海域執(zhí)行護航任務(wù)，這次執(zhí)行任務(wù)的艦艇是從南海艦隊中選擇的：從A“太倉”號、B“徽山湖”號、C“撫仙湖”號中隨機選擇一艘補給艦；再從D“武漢”號、E”蘭州“號、F”�？凇疤栔须S機選擇兩艘導(dǎo)彈驅(qū)逐艦．
（1）請用樹狀圖或列舉法說明中國海軍艦艇編隊符合上述條件的所有可能的選擇方式（用字母表示）；
（2）在（1）的選擇方式中，求中國海軍艦艇編隊恰好選中B“徽山湖”號，同時選中D“武漢”號和 F“�？凇碧杻伤覍�(dǎo)彈驅(qū)逐艦的概率．

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精英家教網(wǎng)2009年12月26日開通的“武廣高鐵”客運專線，使武漢到廣州的時間比原先快速列車縮短了8小時，武漢到廣州的距離為1068.6千米，若客運專線列車的速度是特快列車速度的3倍，那么客運專線列車的速度是多少？

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（2013•沈陽一模）2012年12月26日京廣高鐵全線通車．一列往返于北京和廣州的火車，沿途要經(jīng)過石家莊、鄭州、武漢、長沙四站，鐵路部門要為這趟列車準備印制（　�。┓N車票．

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