·¢²¼Ê±¼ä : ÐÇÆÚËÄ ÎÄÕÂÔ²µÄѧ°¸¸üÐÂÍê±Ï¿ªÊ¼ÔĶÁ
3. ·´±ÈÀýº¯Êýy?
k
µÄͼÏó¾¹ýµãA(2,3). x
£¨1£©ÇóÕâ¸öº¯ÊýµÄ½âÎöʽ£»
£¨2£©ÇëÅжϵãB(1,6)ÊÇ·ñÔÚÕâ¸ö·´±ÈÀýº¯ÊýµÄͼÏóÉÏ£¬²¢ËµÃ÷ÀíÓÉ.
4. ÔÚѹÁ¦²»±äµÄÇé¿öÏ£¬Ä³Îï³ÐÊܵÄѹǿP£¨Pa£©ÊÇËüµÄÊÜÁ¦Ãæ»ýS£¨m2£©µÄ·´±ÈÀýº¯Êý£¬
ÆäͼÏóÈçÓÒͼËùʾ.
£¨1£©ÇóPÓëSÖ®¼äµÄº¯Êý¹Øϵʽ£» £¨2£©Çóµ±S=0.5m2ʱÎïÌåËùÊܵÄѹǿP.
85. Èçͼ£¬·´±ÈÀýº¯Êýy??ÓëÒ»´Îº¯Êýy??x?2µÄͼy xA Ïó½»ÓÚA¡¢BÁ½µã.
D £¨1£©ÇóA¡¢BÁ½µãµÄ×ø±ê£» £¨2£©Çó¡÷AOBµÄÃæ»ý.
O x
B
ÄÜÁ¦Ìá¸ßÁ·Ï°
P y Ò»¡¢Ñ§¿ÆÄÚ×ÛºÏÌâ
1. ÈçÓÒͼ£¬¡÷OPQÊDZ߳¤Îª2µÄµÈ±ßÈý½ÇÐΣ¬Èô·´±ÈÀýº¯ÊýµÄͼ
Ïó¹ýµãP£¬ÔòËüµÄ½âÎöʽÊÇ_____________. 2. ÒÑÖª·´±ÈÀýº¯Êýy?k(k?0)ºÍÒ»´Îº¯Êýy??x?6. O x£¨1£©ÈôÒ»º¯ÊýºÍ·´±ÈÀýº¯ÊýµÄͼÏó½»ÓÚµã(?3,m)£¬ÇómºÍkµÄÖµ.
Q x £¨2£©µ±kÂú×ãʲôÌõ¼þʱ£¬ÕâÁ½¸öº¯ÊýµÄͼÏóÓÐÁ½¸ö²»Í¬µÄ½»µã£¿
£¨3£©µ±k??2ʱ£¬É裨2£©ÖеÄÁ½¸öº¯ÊýͼÏóµÄ½»µã·Ö±ðΪA¡¢B£¬ÊÔÅжÏA¡¢BÁ½µã
·Ö±ðÔÚµÚ¼¸ÏóÏÞ£¿¡ÏAOBÊÇÈñ½Ç»¹ÊǶ۽ǣ¨Ö»ÒªÇóÖ±½Óд³ö½áÂÛ£©£¿
¶þ¡¢Ñ§¿Æ¼ä×ÛºÏÌâ
3. ÈôÒ»¸öԲ׶µÄ²àÃæ»ýΪ20£¬ÔòÏÂͼÖбíʾÕâ¸öԲ׶ĸÏß³¤lÓëµ×Ãæ°ë¾¶rÖ®¼äº¯Êý¹Øϵ
µÄÊÇ£¨ £©
17
l l l l O A r O B r O C r O D r
Èý¡¢Êµ¼ÊÓ¦ÓÃÌâ
4. ijµ¥Î»ÎªÏìÓ¦Õþ¸®·¢³öµÄÈ«Ãñ½¡ÉíµÄºÅÕÙ£¬´òËãÔÚ³¤ºÍ¿í·Ö±ðΪ20Ã׺Í11Ã׵ľØÐδó
ÌüÄÚÐÞ½¨Ò»¸ö60ƽ·½Ã׵ľØÐν¡Éí·¿ABCD. ¸Ã½¡Éí·¿µÄËÄÃæǽ±ÚÖÐÓÐÁ½²àÑØÓôóÌüµÄ¾Éǽ±Ú£¨ÈçͼΪƽÃæʾÒâͼ£©£¬ÒÑ֪װÐÞ¾Éǽ±ÚµÄ·ÑÓÃΪ20Ôª/ƽ·½Ã×£¬Ð½¨£¨º¬×°ÐÞ£©Ç½±ÚµÄ·ÑÓÃΪ80Ôª/ƽ·½Ã×. É轡Éí·¿µÄ¸ß A B Ϊ3Ã×£¬Ò»Ãæ¾Éǽ±ÚABµÄ³¤ÎªxÃ×£¬ÐÞ½¨½¡Éí·¿µÄ×ÜͶÈëΪyÔª.
D C £¨1£©ÇóyÓëxµÄº¯Êý¹Øϵʽ£»
11Ã× £¨2£©ÎªÁ˺ÏÀíÀûÓôóÌü£¬ÒªÇó×Ô±äÁ¿x±ØÐëÂú
×ã8¡Üx¡Ü12. µ±Í¶Èë×ʽðΪ4800Ԫʱ£¬ÎÊÀûÓþÉǽ±ÚµÄ×ܳ¤¶ÈΪ¶àÉÙÃ×£¿
20Ã×
5¡¢ÎªÁËÔ¤·À¡°·Çµä¡±£¬Ä³Ñ§Ð£¶Ô½ÌÊÒ²ÉÓÃҩѬÏû¶¾·¨½øÐÐÏû¶¾. ÒÑÖªÒ©ÎïȼÉÕʱ£¬ÊÒÄÚÿÁ¢y(ºÁ¿Ë) ·½Ã׿ÕÆøÖеĺ¬Ò©Á¿y£¨ºÁ¿Ë£©Óëʱ¼äx ·ÖÖÓ£©³ÉÕý±ÈÀý£¬Ò©ÎïȼÉÕÍêºó£¬yÓëx
6 ³É·´±ÈÀý£¨ÈçͼËùʾ£©. ÏÖ²âµÃÒ©Îï8·Ö
ÖÓȼ±Ï£¬´ËʱÊÒÄÚ¿ÕÆøÖÐÿÁ¢·½Ã׺¬Ò©Á¿Îª6ºÁ¿Ë. Çë¸ù¾ÝÌâÖÐËùÌṩµÄÐÅÏ¢£¬½â´ðÏÂÁÐÎÊÌ⣺
£¨1£©Ò©ÎïȼÉÕʱ£¬y¹ØÓÚxµÄº¯Êý¹Ø
ϵʽΪ£º___________________£¬×Ô±äÁ¿xµÄÈ¡Öµ·¶Î§ÊÇ£ºO 8 x(·ÖÖÓ) ______________£»Ò©ÎïȼÉÕºóy
¹ØÓÚxµÄº¯Êý¹ØϵʽΪ£º___________________£»
£¨2£©Ñо¿±íÃ÷£¬µ±¿ÕÆøÖÐÿÁ¢·½Ã׵ĺ¬Ò©Á¿µÍÓÚ1.6ºÁ¿ËʱѧÉú·½¿É½ø½ÌÊÒ£¬ÄÇô´Ó
Ïû¶¾¿ªÊ¼£¬ÖÁÉÙÐèÒª¾¹ý¼¸·ÖÖÓºó£¬Ñ§Éú²ÅÄܻص½½ÌÊÒ£» £¨3£©Ñо¿±íÃ÷£¬µ±¿ÕÆøÖÐÿÁ¢·½Ã׵ĺ¬Ò©Á¿²»µÍÓÚ3ºÁ¿ËÇÒ³ÖÐøʱ¼ä²»µÍÓÚ10·ÖÖÓʱ£¬
²ÅÄÜÓÐЧµØɱÃð¿ÕÆøÖеIJ¡¾ú£¬ÄÇô´Ë´ÎÏû¶¾ÊÇ·ñÓÐЧ£¿ÎªÊ²Ã´£¿
18
¶þ´Îº¯Êý½Ì°¸
¿ÎÌ⣺2.1¶þ´Îº¯Êý
½ÌѧĿ±ê£º
1¡¢ ´Óʵ¼ÊÇé¾°ÖÐÈÃѧÉú¾Àú̽Ë÷·ÖÎöºÍ½¨Á¢Á½¸ö±äÁ¿Ö®¼äµÄ¶þ´Îº¯Êý¹ØϵµÄ¹ý³Ì£¬½øÒ»²½
ÌåÑéÈçºÎÓÃÊýѧµÄ·½·¨È¥ÃèÊö±äÁ¿Ö®¼äµÄÊýÁ¿¹Øϵ¡£ 2¡¢ Àí½â¶þ´Îº¯ÊýµÄ¸ÅÄÕÆÎÕ¶þ´Îº¯ÊýµÄÐÎʽ¡£
3¡¢ »á½¨Á¢¼òµ¥µÄ¶þ´Îº¯ÊýµÄÄ£ÐÍ£¬²¢Äܸù¾Ýʵ¼ÊÎÊÌâÈ·¶¨×Ô±äÁ¿µÄÈ¡Öµ·¶Î§¡£ 4¡¢ »áÓôý¶¨ÏµÊý·¨Çó¶þ´Îº¯ÊýµÄ½âÎöʽ¡£ ½ÌѧÖص㣺¶þ´Îº¯ÊýµÄ¸ÅÄîºÍ½âÎöʽ
½ÌѧÄѵ㣺±¾½Ú¡°ºÏ×÷ѧϰ¡±Éæ¼°µÄʵ¼ÊÎÊÌâÓеĽÏΪ¸´ÔÓ£¬ÒªÇóѧÉúÓнÏÇ¿µÄ¸ÅÀ¨ÄÜÁ¦¡£ ½ÌѧÉè¼Æ£º
Ò»¡¢´´ÉèÇé¾³£¬µ¼ÈëпÎ
ÎÊÌâ1¡¢ÏÖÓÐÒ»¸ù12m³¤µÄÉþ×Ó£¬ÓÃËüΧ³ÉÒ»¸ö¾ØÐΣ¬ÈçºÎΧ·¨£¬²Åʹ¾ÙÐеÄÃæ»ý×î´ó£¿Ð¡Ã÷ͬѧÈÏΪµ±Î§³ÉµÄ¾ØÐÎÊÇÕý·½ÐÎʱ £¬ËüµÄÃæ»ý×î´ó£¬Ëû˵µÄÓеÀÀíÂð£¿
ÎÊÌâ2¡¢ºÜ¶àͬѧ¶¼Ï²»¶´òÀºÇò£¬ÄãÖªµÀÂð£ºÍ¶ÀºÊ±£¬ÀºÇòÔ˶¯µÄ·ÏßÊÇʲôÇúÏߣ¿ÔõÑù¼ÆËãÀºÇò´ïµ½×î¸ßµãʱµÄ¸ß¶È£¿
ÕâЩÎÊÌⶼ¿ÉÒÔͨ¹ýѧϰ¶í¶þ´Îº¯ÊýµÄÊýѧģÐÍÀ´½â¾ö£¬½ñÌìÎÒÃÇѧϰ¡°¶þ´Îº¯Êý¡±£¨°åÊé¿ÎÌ⣩
¶þ¡¢ºÏ×÷ѧϰ£¬Ì½Ë÷ÐÂÖª
ÇëÓÃÊʵ±µÄº¯Êý½âÎöʽ±íʾÏÂÁÐÎÊÌâÖÐÇé¾°ÖеÄÁ½¸ö±äÁ¿yÓëxÖ®¼äµÄ¹Øϵ£º £¨1£©Ãæ»ýy (cm2)ÓëÔ²µÄ°ë¾¶ x ( Cm )
(2)ÍõÏÈÉú´æÈËÒøÐÐ2ÍòÔª,ÏÈ´æÒ»¸öÒ»Ä궨ÆÚ£¬Ò»ÄêºóÒøÐн«±¾Ï¢×Ô¶¯×ª´æΪÓÖÒ»¸öÒ»Ä궨ÆÚ,ÉèÒ»Ä궨ÆÚµÄÄê´æ¿îÀûÂÊΪÎÄ x Á½ÄêºóÍõÏÈÉú¹²µÃ±¾Ï¢yÔª;
(3)Ä⽨ÖеÄÒ»¸öÎÂÊÒµÄƽÃæͼÈçͼ,Èç¹ûÎÂÊÒÍâΧÊÇÒ»¸ö¾ØÐΣ¬Öܳ¤Îª12Om , ÊÒÄÚͨµÀµÄ³ß´çÈçͼ,ÉèÒ»Ìõ±ß³¤Îª x (cm), ÖÖÖ²Ãæ»ýΪ y (m2)
1 1 1 x
3
£¨Ò»£© ½Ìʦ×éÖ¯ºÏ×÷ѧϰ»î¶¯£º
1¡¢ ÏȸöÌå̽Ç󣬳¢ÊÔд³öyÓëxÖ®¼äµÄº¯Êý½âÎöʽ¡£
2¡¢ ÉÏÊöÈý¸öÎÊÌâÏÈÒ׺óÄÑ£¬ÔÚ¸öÌå̽ÇóµÄ»ù´¡ÉÏ£¬Ð¡×é½øÐкÏ×÷½»Á÷£¬¹²Í¬Ì½ÌÖ¡£ £¨1£©y =¦Ðx2 £¨2£©y = 2000(1+x)2 = 20000x2+40000x+20000 (3) y = (60-x-4)(x-2)=-x2+58x-112
£¨¶þ£©ÉÏÊöÈý¸öº¯Êý½âÎöʽ¾ßÓÐÄÄЩ¹²Í¬ÌØÕ÷£¿ ÈÃѧÉú³ä·Ö·¢±íÒâ¼û£¬Ìá³ö¸÷×Ô¿´·¨¡£
½Ìʦ¹éÄÉ×ܽ᣺ÉÏÊöÈý¸öº¯Êý½âÎöʽ¾»¯¼òºó¶¼¾ßy=ax2+bx+c (a,b,cÊdz£Êý, a¡Ù0)µÄÐÎʽ.
19
°åÊ飺ÎÒÃÇ°ÑÐÎÈçy=ax2+bx+c(ÆäÖÐa,b,CÊdz£Êý£¬a¡Ù0)µÄº¯Êý½Ð×ö¶þ´Îº¯Êý(quadratic funcion)
³ÆaΪ¶þ´ÎÏîϵÊý£¬ bΪһ´ÎÏîϵÊý£¬cΪ³£ÊýÏ
Çë½²³öÉÏÊöÈý¸öº¯Êý½âÎöʽÖеĶþ´ÎÏîϵÊý¡¢Ò»´ÎÏîϵÊýºÍ³£ÊýÏî £¨¶þ£© ×öÒ»×ö
1¡¢ ÏÂÁк¯ÊýÖУ¬ÄÄЩÊǶþ´Îº¯Êý£¿ (1)y?x (2) y??2212 (3) y?2x?x?1 £¨4£©y?x(1?x) 2x£¨5£©y?(x?1)?(x?1)(x?1)
2¡¢·Ö±ð˵³öÏÂÁжþ´Îº¯ÊýµÄ¶þ´ÎÏîϵÊý¡¢Ò»´ÎÏîϵÊýºÍ³£ÊýÏ £¨1£©y?x?1 £¨2£©y?3x?7x?12 £¨3£©y?2x(1?x) 3¡¢Èôº¯Êýy?(m2?1)xmÈý¡¢ÀýÌâʾ·¶£¬Á˽â¹æÂÉ
Àý1¡¢ÒÑÖª¶þ´Îº¯Êý y?x?px?qµ±x=1ʱ£¬º¯ÊýÖµÊÇ4£»µ±x=2ʱ£¬º¯ÊýÖµÊÇ-5¡£ÇóÕâ¸ö¶þ´Îº¯ÊýµÄ½âÎöʽ¡£
´ËÌâÄѶȽÏС£¬µ«È´·´Ó³ÁËÇó¶þ´Îº¯Êý½âÎöʽµÄÒ»°ã·½·¨£¬¿ÉÈÃѧÉúÒ»±ß˵£¬½Ìʦһ±ß°åÊéʾ·¶£¬Ç¿µ÷Êéд¸ñʽºÍ˼¿¼·½·¨¡£
Á·Ï°£ºÒÑÖª¶þ´Îº¯Êýy?ax?bx?c £¬µ±x=2ʱ£¬º¯ÊýÖµÊÇ3£»µ±x=-2ʱ£¬º¯ÊýÖµÊÇ2¡£ÇóÕâ¸ö¶þ´Îº¯ÊýµÄ½âÎöʽ¡£
Àý2¡¢Èçͼ£¬Ò»ÕÅÕý·½ÐÎÖ½°åµÄ±ß³¤Îª2cm£¬½«Ëü¼ôÈ¥4¸öÈ«µÈµÄÖ±½ÇÈý½ÇÐΣ¨Í¼ÖÐÒõÓ°²¿·Ö£©¡£ÉèAE=BF=CG=DH=x(cm) ,ËıßÐÎEFGHµÄÃæ»ýΪy(cm2),Çó£º £¨1£© y¹ØÓÚx µÄº¯Êý½âÎöʽºÍ×Ô±äÁ¿xµÄÈ¡Öµ·¶Î§¡£
£¨2£© µ±x·Ö±ðΪ0.25£¬0.5£¬1.5£¬1.75ʱ£¬¶ÔÓ¦µÄËıßÐÎEFGHµÄÃæ»ý£¬²¢Áбí±íʾ¡£
22222?mΪ¶þ´Îº¯Êý£¬ÔòmµÄֵΪ ¡£
D H
G C
F
A
E
B
·½·¨£º
£¨1£©Ñ§Éú¶ÀÁ¢·ÖÎö˼¿¼£¬³¢ÊÔд³öy¹ØÓÚxµÄº¯Êý½âÎöʽ£¬½ÌʦѲ»Ø¸¨µ¼£¬ÊÊʱµã²¦¡£ £¨2£©¶ÔÓÚµÚÒ»¸öÎÊÌâ¿ÉÒÔÓöàÖÖ·½·¨½â´ð£¬±ÈÈ磺
20