ijְҵѧУÈýÃûѧÉúµ½Ä³³¬ÊвμÓÁËÉç»áʵ¼ù»î¶¯£¬ÔڻÖÐËûÃDzÎÓëÁËijÖÖË®¹ûµÄÏúÊÛ¹¤×÷£¬ÒÑÖª¸ÃË®¹ûµÄ½ø¼ÛΪ8Ôª/ǧ¿Ë£¬ÏÂÃæÊÇËûÃÇÔڻ½áÊøºóµÄ¶Ô»°¡£A£ºÈç¹ûÒÔ10Ôª/ǧ¿ËµÄ-¾ÅÄ꼶Êýѧ
¡ày=ax2+bx+c
=a(x2+b/ax+c/a)
=a[x2-(x1+x2)x+x1?x2]
=a(x-x1)(x-x2).
ÖØÒª¸ÅÄ
a£¬b£¬cΪ³£Êý£¬a¡Ù0£¬ÇÒa¾ö¶¨º¯ÊýµÄ¿ª¿Ú·½Ïò¡£a>0ʱ£¬¿ª¿Ú·½ÏòÏòÉÏ£»
a<0ʱ£¬¿ª¿Ú·½ÏòÏòÏ¡£aµÄ¾ø¶ÔÖµ¿ÉÒÔ¾ö¶¨¿ª¿Ú´óС¡£
aµÄ¾ø¶ÔÖµÔ½´ó¿ª¿Ú¾ÍԽС£¬aµÄ¾ø¶ÔֵԽС¿ª¿Ú¾ÍÔ½´ó¡£
ÄÜÁé»îÔËÓÃÕâÈýÖÖ·½Ê½Çó¶þ´Îº¯ÊýµÄ½âÎöʽ£»
ÄÜÊìÁ·µØÔËÓöþ´Îº¯ÊýÔÚ¼¸ºÎÁìÓòÖеÄÓ¦Óã»
ÄÜÊìÁ·µØÔËÓöþ´Îº¯Êý½â¾öʵ¼ÊÎÊÌâ¡£
¢ÙÅ£¶Ù²åÖµ¹«Ê½:
f(x)=f[x0]+f[x0,x1](x-x0)+f[x0,x1,x2](x-x0)(x-x1)+...f[x0,...xn](x-x0)...(x-xn-1)+Rn(x)ÓÉ´Ë¿ÉÒýµ¼³ö½»µãʽµÄϵÊýa=y/(x¡¤x)(yΪ½Ø¾à)¡¡
¶þ´Îº¯Êý±í´ïʽµÄÓÒ±ßͨ³£Îª¶þ´ÎÈýÏîʽ¡£
Ë«¸ùʽ
y=a(x-x1)*(x-x2)
Èôax2+bx+c=0ÓÐÁ½¸öʵ¸ùx1,x2£¬Ôòy=a(x-x1)(x-x2)´ËÅ×ÎïÏߵĶԳÆÖáΪֱÏßx=(x1+x2)/2¡£
¢ÛÈýµãʽ
ÒÑÖª¶þ´Îº¯ÊýÉÏÈý¸öµã£¬£¨x1,f(x1)£©£¨x2,f(x2)£©£¨x3,f(x3)£©
Ôòf(x)=f(x3)(x-x1)(x-x2)/(x3-x1)(x3-x2)+f(x2)(x-x1)*(x-x3)/(x2-x1)(x2-x3)+f(x1)(x-x2)(x-x3)/(x1-x2)(x1-x3)
ÓëXÖá½»µãµÄÇé¿ö
µ±¡÷=b2-4ac>0ʱ£¬º¯ÊýͼÏñÓëxÖáÓÐÁ½¸ö½»µã¡£(x1,0), (x2,0);
µ±¡÷=b2-4ac=0ʱ£¬º¯ÊýͼÏñÓëxÖáÖ»ÓÐÒ»¸ö½»µã¡£(-b/2a£¬0)¡£
¦¤=b2-4ac<0ʱ£¬Å×ÎïÏßÓëxÖáûÓн»µã¡£
XµÄÈ¡ÖµÊÇÐéÊý£¨x=-b¡À¡Ìb2£4acµÄÖµµÄÏà·´Êý£¬³ËÉÏÐéÊýi£¬Õû¸öʽ×Ó³ýÒÔ2a£©
¶þ´Îº¯Êý½âÊÍʽµÄÇ󷨣º
¾ÍÒ»°ãʽy=ax2£«bx£«c£¨ÆäÖÐa£¬b£¬cΪ³£Êý£¬ÇÒa¡Ù0£©¶øÑÔ£¬ÆäÖк¬ÓÐÈý¸ö´ý¶¨µÄϵÊýa £¬b £¬c£®Çó¶þ´Îº¯ÊýµÄÒ»°ãʽʱ£¬±ØÐëÒªÓÐÈý¸ö¶ÀÁ¢µÄ¶¨Á¿Ìõ¼þ£¬À´½¨Á¢¹ØÓÚa £¬b £¬c µÄ·½³Ì£¬ÁªÁ¢Çó½â£¬ÔÙ°ÑÇó³öµÄa £¬b £¬c µÄÖµ·´´ú»ØÔº¯Êý½âÎöʽ£¬¼´¿ÉµÃµ½ËùÇóµÄ¶þ´Îº¯Êý½âÎöʽ¡£
1.ÇÉÈ¡½»µãʽ·¨£º
֪ʶ¹éÄÉ£º¶þ´Îº¯Êý½»µãʽ£ºy£½a(x£x1)(x£x2) £¨a¡Ù0£©x1£¬x2·Ö±ðÊÇÅ×ÎïÏßÓëxÖáÁ½¸ö½»µãµÄºá×ø±ê¡£
ÒÑÖªÅ×ÎïÏßÓëxÖáÁ½¸ö½»µãµÄºá×ø±êÇó¶þ´Îº¯Êý½âÎöʽʱ£¬Óý»µãʽ±È½Ï¼ò±ã¡£
¢ÙµäÐÍÀýÌâÒ»£º¸æËßÅ×ÎïÏßÓëxÖáµÄÁ½¸ö½»µãµÄºá×ø±ê£¬ºÍµÚÈý¸öµã£¬¿ÉÇó³öº¯ÊýµÄ½»µãʽ¡£
Àý£ºÒÑÖªÅ×ÎïÏßÓëxÖá½»µãµÄºá×ø±êΪ-2ºÍ1 £¬ÇÒͨ¹ýµã£¨2£¬8£©£¬Çó¶þ´Îº¯ÊýµÄ½âÎöʽ¡£
µã²¦£º
½âÉ躯ÊýµÄ½âÎöʽΪy£½a(x+2)(x-1)£¬
¡ß¹ýµã£¨2£¬8£©£¬
¡à8£½a(2+2)(2-1)¡£
½âµÃa=2£¬
¡àÅ×ÎïÏߵĽâÎöʽΪ£º
y£½2(x+2)(x-1)£¬
¼´y£½2x2+2x-4¡£
¢ÚµäÐÍÀýÌâ¶þ£º¸æËßÅ×ÎïÏßÓëxÖáµÄÁ½¸ö½»µãÖ®¼äµÄ¾àÀëºÍ¶Ô³ÆÖᣬ¿ÉÀûÓÃÅ×ÎïÏߵĶԳÆÐÔÇó½â¡£
Àý£ºÒÑÖª¶þ´Îº¯ÊýµÄ¶¥µã×ø±êΪ£¨3£¬-2£©£¬²¢ÇÒͼÏóÓëxÖáÁ½½»µã¼äµÄ¾àÀëΪ4£¬Çó¶þ´Îº¯ÊýµÄ½âÎöʽ¡£
µã²¦£º
ÔÚÒÑÖªÅ×ÎïÏßÓëxÖáÁ½½»µãµÄ¾àÀëºÍ¶¥µã×ø±êµÄÇé¿öÏ£¬ÎÊÌâ±È½ÏÈÝÒ×½â¾ö£®Óɶ¥µã×ø±êΪ£¨3£¬-2£©µÄÌõ¼þ£¬Ò×ÖªÆä¶Ô³ÆÖáΪx£½3£¬ÔÙÀûÓÃÅ×ÎïÏߵĶԳÆÐÔ£¬¿É֪ͼÏóÓëxÖáÁ½½»µãµÄ×ø±ê·Ö±ðΪ£¨1£¬0£©ºÍ£¨5£¬0£©¡£´Ëʱ£¬¿ÉʹÓöþ´Îº¯ÊýµÄ½»µãʽ£¬µÃ³öº¯Êý½âÎöʽ¡£
2.ÇÉÓö¥µãʽ£º
¶¥µãʽy=a(x£h)2+k£¨a¡Ù0£©£¬ÆäÖУ¨h£¬k£©ÊÇÅ×ÎïÏߵĶ¥µã¡£µ±ÒÑÖªÅ×ÎïÏ߶¥µã×ø±ê»ò¶Ô³ÆÖᣬ»òÄܹ»ÏÈÇó³öÅ×ÎïÏ߶¥µãʱ£¬É趥µãʽ½âÌâÊ®·Ö¼ò½à£¬ÒòΪÆäÖÐÖ»ÓÐÒ»¸öδ֪Êýa¡£ÔÚ´ËÀàÎÊÌâÖУ¬³£ºÍ¶Ô³ÆÖᣬ×î´óÖµ»ò×îСֵ½áºÏÆðÀ´ÃüÌâ¡£ÔÚÓ¦ÓÃÌâÖУ¬Éæ¼°µ½ÇŹ°¡¢ËíµÀ¡¢µ¯µÀÇúÏß¡¢Í¶ÀºµÈÎÊÌâʱ£¬Ò»°ãÓö¥µãʽ·½±ã£®
¢ÙµäÐÍÀýÌâÒ»£º¸æË߶¥µã×ø±êºÍÁíÒ»¸öµãµÄ×ø±ê£¬Ö±½Ó¿ÉÒÔ½â³öº¯Êý¶¥µãʽ¡£
Àý£ºÒÑÖªÅ×ÎïÏߵĶ¥µã×ø±êΪ£¨-1£¬-2£©£¬ÇÒͨ¹ýµã£¨1£¬10£©£¬Çó´Ë¶þ´Îº¯ÊýµÄ½âÎöʽ¡£
µã²¦£º
½â¡ß¶¥µã×ø±êΪ£¨-1£¬-2£©£¬
¹ÊÉè¶þ´Îº¯Êý½âÎöʽΪy=a(x+1)2-2 £¨a¡Ù0£©¡£
°Ñµã£¨1£¬10£©´úÈëÉÏʽ£¬µÃ10=a¡¤(1+1)2-2¡£
¡àa=3¡£
¡à¶þ´Îº¯ÊýµÄ½âÎöʽΪy=3(x+1)2-2£¬¼´y=3x2+6x+1¡£
¢ÚµäÐÍÀýÌâ¶þ£º
Èç¹ûa>0£¬ÄÇôµ± ʱ£¬yÓÐ×îСֵÇÒy×îС=£»
Èç¹ûa<0£¬ÄÇô£¬µ±Ê±£¬yÓÐ×î´óÖµ£¬ÇÒy×î´ó=¡£
¸æËß×î´óÖµ»ò×îСֵ£¬Êµ¼ÊÉÏÒ²ÊǸæËßÁ˶¥µã×ø±ê£¬Í¬ÑùÒ²¿ÉÒÔÇó³ö¶¥µãʽ¡£
Àý£ºÒÑÖª¶þ´Îº¯Êýµ±x£½4ʱÓÐ×îСֵ£3£¬ÇÒËüµÄͼÏóÓëxÖáÁ½½»µã¼äµÄ¾àÀëΪ6£¬ÇóÕâ¸ö¶þ´Îº¯ÊýµÄ½âÎöʽ¡£
µã²¦£º
Îö½â¡ß¶þ´Îº¯Êýµ±x£½4ʱÓÐ×îСֵ£3£¬¡à¶¥µã×ø±êΪ£¨4£¬-3£©£¬¶Ô³ÆÖáΪֱÏßx£½4£¬Å×ÎïÏß¿ª¿ÚÏòÉÏ¡£
ÓÉÓÚͼÏóÓëxÖáÁ½½»µã¼äµÄ¾àÀëΪ6£¬¸ù¾ÝͼÏóµÄ¶Ô³ÆÐԾͿÉÒԵõ½Í¼ÏóÓëxÖáÁ½½»µãµÄ×ø±êÊÇ£¨1£¬0£©ºÍ£¨7£¬0£©¡£
¡àÅ×ÎïÏߵĶ¥µãΪ£¨4£¬-3£©ÇÒ¹ýµã£¨1£¬0£©¡£
¹Ê¿ÉÉ躯Êý½âÎöʽΪy£½a(x£4)2£3¡£
½«£¨1£¬0£©´úÈëµÃ0£½a(1£4)2£3, ½âµÃa£½13£®
¡ày£½13(x£4)2-3£¬¼´y£½13x2£83x£«73¡£
¢ÛµäÐÍÀýÌâÈý£º¸æË߶ԳÆÖᣬÏ൱ÓÚ¸æËßÁ˶¥µãµÄºá×ø±ê£¬×ÛºÏÆäËûÌõ¼þ£¬Ò²¿É½â³ö¡£
ÀýÈ磺
£¨1£©ÒÑÖª¶þ´Îº¯ÊýµÄͼÏó¾¹ýµãA£¨3£¬-2£©ºÍB£¨1£¬0£©£¬ÇÒ¶Ô³ÆÖáÊÇÖ±Ïßx£½3£®ÇóÕâ¸ö¶þ´Îº¯ÊýµÄ½âÎöʽ.
£¨2£©ÒÑÖª¹ØÓÚxµÄ¶þ´Îº¯ÊýͼÏóµÄ¶Ô³ÆÖáÊÇÖ±Ïßx=1£¬Í¼Ïó½»yÖáÓڵ㣨0£¬2£©£¬ÇÒ¹ýµã£¨-1£¬0£©£¬ÇóÕâ¸ö¶þ´Îº¯ÊýµÄ½âÎöʽ.
£¨3£©ÒÑÖªÅ×ÎïÏߵĶԳÆÖáΪֱÏßx=2£¬ÇÒͨ¹ýµã£¨1£¬4£©ºÍµã£¨5£¬0£©£¬Çó´ËÅ×ÎïÏߵĽâÎöʽ.
£¨4£©¶þ´Îº¯ÊýµÄͼÏóµÄ¶Ô³ÆÖáx=-4£¬ÇÒ¹ýԵ㣬ËüµÄ¶¥µãµ½xÖáµÄ¾àÀëΪ4£¬Çó´Ëº¯ÊýµÄ½âÎöʽ£®
¢ÜµäÐÍÀýÌâËÄ£ºÀûÓú¯ÊýµÄ¶¥µãʽ£¬½âͼÏñµÄƽÒƵÈÎÊÌâ·Ç³£·½±ã¡£
Àý£º°ÑÅ×ÎïÏßy=ax2+bx+cµÄͼÏñÏòÓÒƽÒÆ3 ¸öµ¥Î», ÔÙÏòÏÂƽÒÆ2 ¸öµ¥Î», ËùµÃͼÏñµÄ½âÎöʽÊÇy=x2-3x+5, Ôòº¯ÊýµÄ½âÎöʽΪ_______¡£
µã²¦£º
½âÏȽ«y=x2-3x+5»¯Îªy=(x-32)2+5-94, ¼´y=(x-32)2+114¡£
¡ßËüÊÇÓÉÅ×ÎïÏßµÄͼÏñÏòÓÒƽÒÆ3 ¸öµ¥Î», ÔÙÏòÏÂƽÒÆ2 ¸öµ¥Î»µÃµ½µÄ£¬
¡àÔÅ×ÎïÏߵĽâÎöʽÊÇy=(x-32+3)2+114+2=(x+32)2+194=x2+3x+7¡£
- ×îÐÂÄÚÈÝ
- Ïà¹ØÄÚÈÝ
- ÍøÓÑÍƼö
- ͼÎÄÍƼö
[¼Ò³¤½ÌÓý] º¢×ÓΪʲô»áºÍ¸¸Ä¸¸ÐÇéÊèÀ룿 (2019-07-14) |
[½Ìʦ·ÖÏí] ¸øÔ¶·½½ã½ãµÄÒ»·âÐÅ (2018-11-07) |
[½Ìʦ·ÖÏí] ÉìËõÃÅ (2018-11-07) |
[½Ìʦ·ÖÏí] »Ø¼ÒÏç (2018-11-07) |
[½Ìʦ·ÖÏí] ÊÇ·çζҲÊÇÈ˼ä (2018-11-07) |
[½Ìʦ·ÖÏí] Ò»¾ä¸ñÑÔµÄÆôʾ (2018-11-07) |
[½Ìʦ·ÖÏí] ÎÞ¹æ¾Ø²»³É·½Ô² (2018-11-07) |
[½Ìʦ·ÖÏí] µÚÊ®½ìÈ«¹ú½ÌÓýÃû¼ÒÂÛ̳ÓиУ¨¶þ£© (2018-11-07) |
[½Ìʦ·ÖÏí] Ì°ÍæµÄС¹· (2018-11-07) |
[½Ìʦ·ÖÏí] δÃüÃûÎÄÕ (2018-11-07) |