单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,有约束条件的二次函数的最值问题,有约束条件的二次函数的最值问题,给定二次函数:,y=2x,2,-8x+1,,我们怎么求它的最值。,O,x,y,2,-,7,解,:y=2,(,x-2,),2,-7,,,由图象知,当,x=2,时,,y,有最小值,,y,min,=f,(,2,),=-7,,,没有最大值。,小结、,二次函数,y=ax,2,+bx+c,(,a0,)中,,y,取得最小值,当自变量,x=,时,,给定二次函数:y=2x2-8x+1,我们怎么求它的最值。,4,例,1.,当,x2,,,4,时,求函数,y=f,(,x,),=2x,2,-8x+1,的最值。,因,y=2(x,2),2,7,,是否当,x=2,时,,y,取得最小值?为什么?,2,O,x,y,-,7,分析:此题和上题有何不同,4 例1.当x2,4时,求函数y=f(x)=2x2-8,4,-1,变,1,:,x-1,,,4,时,求函数,y=f,(,x,),=2x,2,-8x+1,的最小值、最大值。,2,O,x,y,-,7,分析,:,由图象知,当,x=2,时,,y,有最小值,,y,min,=f,(,2,),=-7,,,当,x=-1,时,,y,有最大值,,y =f,(,-1,),=11,,,max,4-1变1:x-1,4时,求函数y=f(x)=2x2-,变,2:,x,2,,,0,时,求函数,y=f,(,x,),=2x,2,-8x+1,的最小值、最大值。,4,-2,2,O,x,y,-,7,分析,:,由图象知,当,x=0,时,,y,有最小值,,y,min,=f,(,0,),=1,,,当,x=-2,时,,y,有最大值,,y =f,(,-2,),=25,,,max,变2:x2,0时,求函数y=f(x)=2x2-8x,小结、,求给定区间,xa,,,b,的二次函数,y=f(x)=ax,2,+bx+c,(,a0,)最值步骤,,,(,1,)配方。,(,2,)画图象。,(,3,)根据图象确定函数最值。,(看所给区间内的最高点和最低点),小结、求给定区间xa,b的二次函数y=f(x)=ax2,-3,2,例,2.,已知函数,f(x)=x,2,+2x+a(-3x2),的最小值是,4,,求,a,的值。,-1,O,x,y,变,1,:,若最大值为,8,求,a,的值,解,:f(x)=x,2,+2x+a,的对称轴为,x=,1,,,f(x),在,0,,,2,上单调递增,,f(x),的最小值为,f(0)=a,,即,a=4,-32例2.已知函数f(x)=x2+2x+a(-3x2),2,变,2,:,已知函数,f(x)=x,2,+2x+a(,0 x2,),的最小值是,4,,求,a,的值。,-1,O,x,y,解,:,f(x)=x,2,+2x+a,的对称轴为,x=,1,,,f(x),在,0,,,2,上单调递增,,f(x),的最小值为,f(0)=a,,即,a=4,2变2:已知函数f(x)=x2+2x+a(0 x2)的最小,2,变,3,:,已知,x,2,+2x+a,4,在,x,0,,,2,上恒成立,求,a,的值。,-1,O,x,y,解,:,令,f(x)=x,2,+2x+a,它,的对称轴为,x=,1,,,f(x),在,0,,,2,上单调递增,,f(x),的最小值为,f(0)=a,,即,a,4,2变3:已知x2+2x+a4在x 0,2上恒成立,求,变,4,:,已知 在,x,0,,,2,上恒成立,求,a,的值。,log,2,x,2,+2x+a,2,变4:已知 在x 0,2lo,例,3,:若,x,,求函数,y=x,2,+ax+3,的最小值:,O,1,x,y,-1,例3:若x,例,3,:若,x,,求函数,y=x,2,+ax+3,的最值:,-1,1,O,x,y,例3:若x,例,3,:若,x,,求函数,y=x,2,+ax+3,的最值:,-1,1,O,x,y,例3:若x,例,3,:若,x,,求函数,y=x,2,+ax+3,的最值:,O,x,y,1,-1,当 即,a,2,时,y,的最小值为,f(-1),=4-,a,例3:若x,例,3,:若,x,,求函数,y=x,2,+ax+3,的最小值:,O,x,y,1,-1,(2),当,即,0,a,2,时,y,的最小值为,f(),例3:若x,例,3,:若,x,,求函数,y=x,2,+ax+3,的最值:,O,x,y,1,-1,(4),当 即,a,-2,时,y,的最小值为,f(1),=4+,a,y,的最大值为,f(-1),=4-,a,函数在,-1,1,上是减函数,例3:若x,1.,已知,y=,x,2,+ax+3,,,x,1,1,,,求,y,的最大值,x,O,1,-1,y,练一练,2,、当,a,为何值时,函数,y=f,(,x,),=,x,2,-2ax+a,2,-2a+6,在,x3,,,4,时的值恒大于,0,?,1.已知y=x2+ax+3,x1,1,xO1-1,谢谢各位光临,谢谢各位光临,Do you like bananas?,Section A,Unit 9,Do you like bananas?Section A,half,an,apple,an,apple,three apple,s,half an applean apple thr,a piece of,orange,two,orange,s,a piece of orange two or,three tomato,es,a piece of,tomato,three tomatoesa piece of tomat,six pear,s,some banana,s,six pearssome bananas,a strawberry,many strawberr,ies,a strawberry many,a potato,French fr,ies,potato,es,=potato chip,s,a potato French friespotat,two hamburger,s,two hamburgers,broccoli,some broccoli,broccolisome broccoli,salad,salad,ice cream,ice cream,pear,banana,orange,strawberry,French fry,hamburger,salad,ice cream,tomato,broccoli,s,s,s,s,es,ies,ies,pearbananaorangestrawberryFren,Match the words with the pictures on page 31.,i,hamburger,s,_,tomato,es,_,broccoli _,French fr,ies,_,orange _,ice cream _,salad _,banana,s,_,strawberr,ies,_,pear,s,_,d,g,a,h,e,f,c,b,j,Match the words with the pictu,Do,you like?,Yes,I/we,do,.,No,I/we,dont,.,Yes,I/we,do,.,Yes,I/we,do,.,Yes,I/we,do,.,No,I/we,dont,.,No,I/we,dont,.,No,I/we,dont,.,Do you like?Yes,I/we,Do,you like?,Do you like?,Do,you like?,Yes,I,do,.,No,I,dont,.,Yes,we,do,.,Yes,they,do,.,No,they,dont,.,No,we,dont,.,Do,they like?,Do you like?Yes,Does,she like?,Does,he like?,Yes,he,does,.,No,he,doesnt,.,Yes,she,does,.,No,she,doesnt,.,Does she like?Does,Do,you like bananas?,Yes,I/we,do,.,No,I/we,dont,.,Do,they like oranges?,Yes,they,do,.,No,they,dont,.,Does,he like broccoli?,Yes,he,does,.,No,he,doesnt,.,Does,she like apples?,Yes,she,does,.,No,she,doesnt,.,Do you like bananas?Yes,I/we,Listen and number the conversations(1-3).,A:Do you like salad?,B:No,I dont.,A:Do you like bananas?,B:Yes,I do.,A:Do you like oranges?,B:Yes,I do.,1,2,3,Listen and number the conversa,bananas,oranges,strawberries,French fries,hamburgers,salad,ice cream,tomatoes,broccoli,name,food,pears,结束放映,bananasorangesstrawberr,S1,S2,S3,S4,apples,bananas,oranges,strawberries,French fries,hamburgers,salad,ice cream,tomatoes,broccoli,name,food,pears,S1 S2 S3 S4 applesbanana,Homework:,听磁带跟读至少,5,次,背诵默写。(家长签字),制作一份调查表,调查你的家人喜爱的食物。,Homework:听磁带跟读至少5次,背诵默写。(家长签字),