探究一類含參數(shù)二次函數(shù)范圍(最值)問題

1、杭州市源清中學(xué)杭州市源清中學(xué)數(shù)學(xué)組數(shù)學(xué)組 王凱王凱探究一類含參數(shù)二次探究一類含參數(shù)二次函數(shù)范圍（最值）問題函數(shù)范圍（最值）問題2015年年6月月7日日解答題解答題第三題第三題全省全省17.7萬萬2.21分分高考分值分配：高考分值分配：7分分+8分結(jié)構(gòu)分結(jié)構(gòu)0max ()tf x(1)1fxyO2(1)3x2( )22f xxx2( )f xxaxb0max()tf x( 1)3fxyO2(1)3x2( )22f xxx2( )f xxaxbminmax( )( )f xtf x xyO03t 2(1)3x2( )22f xxx2( )f xxaxb0 x310min ()tf x( 1)3f

2、xyO2(1)3x2( )22f xxx2( )f xxaxbxyOmin( )tf x0()0f x2(1)3x2( )22f xxx2( )f xxaxb0 x312(1)3x2( )22f xxxxyOxyO( )max( 1) ,(1)M affmax1,1aa xyO12a 2( )f xxaxb2( )2f xxax( )max( 1) ,(1)M affmax1,1aa 1a2( )f xxaxbmax1,1aaayO1ya1ya 數(shù)缺形時(shí)數(shù)缺形時(shí)少直觀少直觀，形少數(shù)時(shí)，形少數(shù)時(shí)難入微難入微；數(shù)形數(shù)形結(jié)合結(jié)合百般百般好好，隔離分家萬事休。，隔離分家萬事休。( )11M aaa 2

3、( )2f xxax(2)a 2( )f xxaxb2( )1aM aa時(shí)，xyO12a 2a 時(shí)2( )2f xxax2( )f xxaxb2( )1aM aa時(shí)，2a 時(shí)2a 時(shí)2( )1aM aa時(shí)，( )max( 1) ,(1)M affmax1,1aa 1a 2a 時(shí)xyO12a2( )2f xxax12( )12aaM aaa 2( )f xxaxb全省全省17.7萬萬 2.21分分2( )f xxaxb( , )max( 1) ,(1)M a bffmax1,1abab2a xyO12a 2a xyO12aa2變式：變式：2sinsinxaxb2tatb 1,1sinxt 令變式：變式：2sinsinxaxb 1,1sinxt 令2tatb2sinsinxaxb牛刀小試：牛刀小試：2( )(4)3f xxaxa 0max()tf xxyO4(0,2)2a4max(0) ,() ,(1)2afff2(2)max3,14aaa(0,4)a對于任意的成立2min(2)max3,14ataa1牛刀小試：牛刀小試：kyxx類比遷移：類比遷移：222( )+3abf xxaaxa222( )+ 期待你分享給我智慧期待你分享給我智慧