26．解:(1)由已知.得.. . ．．············································································································ 設(shè)過(guò)點(diǎn)的拋物線的解析式為．將點(diǎn)的坐標(biāo)代入.得．將和點(diǎn)的坐標(biāo)分別代入.得 ··································································································· 解這個(gè)方程組.得故拋物線的解析式為．··························································· (2)成立．························································································· 點(diǎn)在該拋物線上.且它的橫坐標(biāo)為. 點(diǎn)的縱坐標(biāo)為．······················································································· 設(shè)的解析式為. 將點(diǎn)的坐標(biāo)分別代入.得解得的解析式為．········································································ .．··························································································· 過(guò)點(diǎn)作于點(diǎn). 則． . ．又. ．．．··········································································································· ． (3)點(diǎn)在上...則設(shè)． ..． ①若.則. 解得．.此時(shí)點(diǎn)與點(diǎn)重合．．··········································································································· ②若.則. 解得 ..此時(shí)軸．與該拋物線在第一象限內(nèi)的交點(diǎn)的橫坐標(biāo)為1. 點(diǎn)的縱坐標(biāo)為．．······································································································· ③若.則. 解得..此時(shí).是等腰直角三角形．過(guò)點(diǎn)作軸于點(diǎn). 則.設(shè). ．．解得．．··········································· 綜上所述.存在三個(gè)滿足條件的點(diǎn). 即或或． 26．如圖.已知拋物線經(jīng)過(guò)點(diǎn).拋物線的頂點(diǎn)為.過(guò)作射線．過(guò)頂點(diǎn)平行于軸的直線交射線于點(diǎn).在軸正半軸上.連結(jié)． (1)求該拋物線的解析式, (2)若動(dòng)點(diǎn)從點(diǎn)出發(fā).以每秒1個(gè)長(zhǎng)度單位的速度沿射線運(yùn)動(dòng).設(shè)點(diǎn)運(yùn)動(dòng)的時(shí)間為．問(wèn)當(dāng)為何值時(shí).四邊形分別為平行四邊形?直角梯形?等腰梯形? (3)若.動(dòng)點(diǎn)和動(dòng)點(diǎn)分別從點(diǎn)和點(diǎn)同時(shí)出發(fā).分別以每秒1個(gè)長(zhǎng)度單位和2個(gè)長(zhǎng)度單位的速度沿和運(yùn)動(dòng).當(dāng)其中一個(gè)點(diǎn)停止運(yùn)動(dòng)時(shí)另一個(gè)點(diǎn)也隨之停止運(yùn)動(dòng)．設(shè)它們的運(yùn)動(dòng)的時(shí)間為.連接.當(dāng)為何值時(shí).四邊形的面積最小?并求出最小值及此時(shí)的長(zhǎng)． *26．解:(1)拋物線經(jīng)過(guò)點(diǎn). ·························································································· 1分二次函數(shù)的解析式為:·················································· 3分 (2)為拋物線的頂點(diǎn)過(guò)作于.則. ··················································· 4分當(dāng)時(shí).四邊形是平行四邊形 ················································ 5分當(dāng)時(shí).四邊形是直角梯形過(guò)作于.則 (如果沒(méi)求出可由求) ····························································································· 6分當(dāng)時(shí).四邊形是等腰梯形綜上所述:當(dāng).5.4時(shí).對(duì)應(yīng)四邊形分別是平行四邊形.直角梯形.等腰梯形．·· 7分及已知.是等邊三角形則過(guò)作于.則········································································· 8分 =·································································································· 9分當(dāng)時(shí).的面積最小值為··································································· 10分此時(shí) ······················································ 11分【查看更多】

已知四邊形ABCD中，P是對(duì)角線BD上的一點(diǎn)，過(guò)P作MN∥AD，EF∥CD，分別交AB、CD、AD、BC于點(diǎn)M、N、E、F，設(shè)a=PM•PE，b=PN•PF，解答下列問(wèn)題：
（1）當(dāng)四邊形ABCD是矩形時(shí)，見(jiàn)圖1，請(qǐng)判斷a與b的大小關(guān)系，并說(shuō)明理由；
（2）當(dāng)四邊形ABCD是平行四邊形，且∠A為銳角時(shí)，見(jiàn)圖2，（1）中的結(jié)論是否成立？并說(shuō)明理由；
（3）在（2）的條件下，設(shè)

BP

PD

=k，是否存在這樣的實(shí)數(shù)k，使得

S平行四邊形PEAM

S△ABD

=

4

9

？若存在，請(qǐng)求出滿足條件的所有k的值；若不存在，請(qǐng)說(shuō)明理由．

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已知：在平面直角坐標(biāo)系xOy中，二次函數(shù)y=x²+bx+c的圖象與x軸交于A、B兩點(diǎn)，點(diǎn)A在點(diǎn)B的左側(cè)，若拋物線的對(duì)稱軸為x=1，點(diǎn)A的坐標(biāo)為（-1，0）．
（1）求這個(gè)二次函數(shù)的解析式；
（2）設(shè)拋物線的頂點(diǎn)為C，拋物線上一點(diǎn)D的坐標(biāo)為（-3，12），過(guò)點(diǎn)B、D的直線與拋物線的對(duì)稱軸交于點(diǎn)E．問(wèn)：是否存在這樣的點(diǎn)F，使得以點(diǎn)B、C、E、F為頂點(diǎn)的四邊形是平行四邊形？若存在，求出點(diǎn)F的坐標(biāo)；若不存在，請(qǐng)說(shuō)明理由；
（3）在（2）的條件下，若在BD上存在一點(diǎn)P，使得直線AP將四邊形ACBD分成了面積相等的兩部分，請(qǐng)你求出此時(shí)點(diǎn)P的坐標(biāo)．

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已知：在平面直角坐標(biāo)系xOy中，二次函數(shù)y=x²+bx+c的圖象與x軸交于A、B兩點(diǎn)，點(diǎn)A在點(diǎn)B的左側(cè)，若拋物線的對(duì)稱軸為x=1，點(diǎn)A的坐標(biāo)為（-1，0）．
（1）求這個(gè)二次函數(shù)的解析式；
（2）設(shè)拋物線的頂點(diǎn)為C，拋物線上一點(diǎn)D的坐標(biāo)為（-3，12），過(guò)點(diǎn)B、D的直線與拋物線的對(duì)稱軸交于點(diǎn)E．問(wèn)：是否存在這樣的點(diǎn)F，使得以點(diǎn)B、C、E、F為頂點(diǎn)的四邊形是平行四邊形？若存在，求出點(diǎn)F的坐標(biāo)；若不存在，請(qǐng)說(shuō)明理由；
（3）在（2）的條件下，若在BD上存在一點(diǎn)P，使得直線AP將四邊形ACBD分成了面積相等的兩部分，請(qǐng)你求出此時(shí)點(diǎn)P的坐標(biāo)．

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已知拋物線y＝x²＋4x＋m(m為常數(shù))經(jīng)過(guò)點(diǎn)(0，4)．

(1)求m的值；

(2)將該拋物線先向右、再向下平移得到另一條拋物線．已知平移后的拋物線滿足下述兩個(gè)條件：它的對(duì)稱軸(設(shè)為直線l₂)與平移前的拋物線的對(duì)稱軸(設(shè)為直線l₁)關(guān)于y軸對(duì)稱；它所對(duì)應(yīng)的函數(shù)的最小值為－8．

①試求平移后的拋物線的解析式；

②試問(wèn)在平移后的拋物線上是否存在點(diǎn)P，使得以3為半徑的圓P既與x軸相切，又與直線l₂相交？若存在，請(qǐng)求出點(diǎn)P的坐標(biāo)，并求出直線l₂被圓P所截得的弦AB的長(zhǎng)度；若不存在，請(qǐng)說(shuō)明理由．

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