ÌâÄ¿ÄÚÈÝ

£¨1£©Çó¶þ´Îº¯ÊýµÄ½âÎöʽ¼°Å×ÎïÏ߶¥µãMµÄ×ø±ê£»
£¨2£©ÈôµãNΪÏ߶ÎBMÉϵÄÒ»µã£¬¹ýµãN×÷xÖáµÄ´¹Ïߣ¬´¹×ãΪµãQ£®µ±µãNÔÚÏ߶ÎBMÉÏÔ˶¯Ê±£¨µãN²»ÓëµãB¡¢µãMÖغϣ©£¬ÉèNQµÄ³¤Îªt£¬ËıßÐÎNQACµÄÃæ»ýΪs£¬ÇósÓëtÖ®¼äµÄº¯Êý¹Øϵʽ¼°×Ô±äÁ¿tÈ¡Öµ·¶Î§£»
£¨3£©½«¡÷OAC²¹³É¾ØÐΣ¬Ê¹¡÷OACµÄÁ½¸ö¶¥µã³ÉΪ¾ØÐÎÒ»±ßµÄÁ½¸ö¶¥µã£¬µÚÈý¸ö¶¥µãÂäÔÚ¾ØÐÎÕâÒ»±ßµÄ¶Ô±ßÉÏ£¬Çó³ö¾ØÐÎδ֪¶¥µãµÄ×ø±ê£®
·ÖÎö£º£¨1£©¸ù¾ÝͼÏó¿ÉÒÔÖªµÀA£¬B£¬CÈýµãµÄ×ø±êÒÑÖª£¬¸ù¾Ý´ý¶¨ÏµÊý·¨¾Í¿ÉÒÔÇó³öº¯ÊýµÄ½âÎöʽ£®½ø¶øÇó³ö¶¥µãMµÄ×ø±ê£®
£¨2£©¸ù¾Ý´ý¶¨ÏµÊý·¨¿ÉÒÔÇó³öÖ±ÏßMBµÄ½âÎöʽ£¬ÉèNQµÄ³¤Îªt£¬¼´NµãµÄ×Ý×ø±êÊÇt£¬°Ñx=t´úÈë½âÎöʽ¾Í¿ÉÒÔÇó³öºá×ø±ê£¬ËıßÐÎNQACµÄÃæ»ýs=S¡÷AOC+SÌÝÐÎOQNC£¬¿ÉÒÔÓÃt·Ö±ð±íʾ³ö¡÷AOCºÍÌÝÐÎOQNCµÄÃæ»ý£¬Òò¶ø¾ÍµÃµ½sÓëtÖ®¼äµÄº¯Êý¹Øϵʽ£®
£¨3£©¿ÉÒÔ²¹³ÉµÄ¾ØÐÎÓÐÁ½ÖÖÇé¿ö£¬¼´Í¼1£¬µÄÇé¿ö£¬Ò×µÃδ֪¶¥µã×ø±êÊǵãD£¨-1£¬2£©£»
ÒÔµãA¡¢µãCΪ¾ØÐεÄÁ½¸ö¶¥µã£¬µÚÈý¸ö¶¥µãʱ£¬ÂäÔÚ¾ØÐÎÕâÒ»±ßACµÄ¶Ô±ßÉÏ£¬ÈçÏÂͼ2£¬Ò×Ö¤Rt¡÷HOC¡×Rt¡÷COA£¬¸ù¾ÝÏàËÆÈý½ÇÐεĶÔÓ¦±ßµÄ±ÈÏàµÈ£¬¾Í¿ÉÒÔÇó³öOHµÄ³¤£¬¸ù¾ÝÖ±ÏßƽÐеĹØϵÀûÓôý¶¨ÏµÊý·¨¾Í¿ÉÒÔÇó³öÖ±ÏßAFÓëÖ±ÏßACµÄ½âÎöʽ£¬Á½º¯ÊýµÄ½»µã£¬¾ÍÊÇÂú×ãÌõ¼þµÄµã£®
£¨2£©¸ù¾Ý´ý¶¨ÏµÊý·¨¿ÉÒÔÇó³öÖ±ÏßMBµÄ½âÎöʽ£¬ÉèNQµÄ³¤Îªt£¬¼´NµãµÄ×Ý×ø±êÊÇt£¬°Ñx=t´úÈë½âÎöʽ¾Í¿ÉÒÔÇó³öºá×ø±ê£¬ËıßÐÎNQACµÄÃæ»ýs=S¡÷AOC+SÌÝÐÎOQNC£¬¿ÉÒÔÓÃt·Ö±ð±íʾ³ö¡÷AOCºÍÌÝÐÎOQNCµÄÃæ»ý£¬Òò¶ø¾ÍµÃµ½sÓëtÖ®¼äµÄº¯Êý¹Øϵʽ£®
£¨3£©¿ÉÒÔ²¹³ÉµÄ¾ØÐÎÓÐÁ½ÖÖÇé¿ö£¬¼´Í¼1£¬µÄÇé¿ö£¬Ò×µÃδ֪¶¥µã×ø±êÊǵãD£¨-1£¬2£©£»
ÒÔµãA¡¢µãCΪ¾ØÐεÄÁ½¸ö¶¥µã£¬µÚÈý¸ö¶¥µãʱ£¬ÂäÔÚ¾ØÐÎÕâÒ»±ßACµÄ¶Ô±ßÉÏ£¬ÈçÏÂͼ2£¬Ò×Ö¤Rt¡÷HOC¡×Rt¡÷COA£¬¸ù¾ÝÏàËÆÈý½ÇÐεĶÔÓ¦±ßµÄ±ÈÏàµÈ£¬¾Í¿ÉÒÔÇó³öOHµÄ³¤£¬¸ù¾ÝÖ±ÏßƽÐеĹØϵÀûÓôý¶¨ÏµÊý·¨¾Í¿ÉÒÔÇó³öÖ±ÏßAFÓëÖ±ÏßACµÄ½âÎöʽ£¬Á½º¯ÊýµÄ½»µã£¬¾ÍÊÇÂú×ãÌõ¼þµÄµã£®
½â´ð£º½â£º£¨1£©ÉèÕâ¸ö¶þ´Îº¯ÊýµÄ½âÎöʽΪ
y=a£¨x+1£©£¨x-2£©£¬£¨1·Ö£©
°ÑµãC£¨0£¬2£©×ø±ê´úÈëÆäÖУ¬ÇóµÃa=-1£¬
y=-£¨x+1£©£¨x-2£©=-x2+x+2=-£¨x-
£©2+
¡àÕâ¸ö¶þ´Îº¯ÊýµÄ½âÎöʽΪ£º
y=-x2+x+2£¨3·Ö£©
¶¥µãMµÄ×ø±êΪM£¨
£¬
£©£»£¨4·Ö£©
[Ò²¿ÉÉèΪһ°ãʽy=ax2+bx+c£¬°ÑA¡¢B¡¢CÈýµã×ø±ê´úÈë½â³ö]
£¨2£©ÉèÏ߶ÎBMËùÔÚÖ±ÏߵĽâÎöʽΪ£ºy=kx+b£¬£¨5·Ö£©
·Ö±ð°ÑB£¨2£¬0£©¡¢M£¨
£¬
£©×ø±ê´úÈëÆäÖУ¬
½âµÃk=-
£¬b=3£¬
¡ày=-
x+3£®
ÈôNµÄ×ø±êΪ£¨x£¬t£©£¬ÔòµÃt=-
x+3£¬
½âµÃx=2-
t£¬£¨6·Ö£©
ÓÉͼÐοÉÖª£ºs=S¡÷AOC+SÌÝÐÎOQNC£¨7·Ö£©
=
¡Á1¡Á2+
£¨2+t£©£¨2-
t£©
»¯¼òÕûÀíµÃs=-
t2+
t+3£¬£¨8·Ö£©
ÆäÖÐ0£¼t£¼
£»£¨9·Ö£©
£¨3£©ÒÔµãO¡¢µãA£¨»òµãO¡¢µãC£©Îª¾ØÐεÄÁ½¸ö¶¥µã£¬
µÚÈý¸ö¶¥µãÂäÔÚ¾ØÐÎÕâÒ»±ßOA£¨»ò±ßOC£©µÄ¶Ô±ßÉÏ£¬
ÈçÏÂͼ1£¬´ËʱÒ×µÃδ֪¶¥µã×ø±êÊǵãD£¨-1£¬2£©£»£¨10·Ö£©
ÒÔµãA¡¢µãCΪ¾ØÐεÄÁ½¸ö¶¥µã£¬µÚÈý¸ö¶¥µã£¨¼´µãO£©
ÂäÔÚ¾ØÐÎÕâÒ»±ßACµÄ¶Ô±ßÉÏ£¬ÈçÏÂͼ2£¬´Ëʱ
δ֪¶¥µã·Ö±ðΪµãE¡¢µãF£®£¨11·Ö£©
ËüÃǵÄ×ø±êÇó½âÈçÏ£º
¡ßACEFΪ¾ØÐΣ¬
¡à¡ÏACEΪֱ½Ç£¬ÑÓ³¤CE½»xÖáÓÚµãH£¬
ÔòÒ×µÃRt¡÷HOC¡×Rt¡÷COA£¬
¡à
=
£¬ÇóµÃOH=4£¬
¡àµãHµÄ×ø±êH£¨4£¬0£©£®¿ÉÇóµÃÏ߶ÎCHËùÔÚÖ±ÏßµÄ
½âÎöʽΪ£ºy=-
x+2£»£¨12·Ö£©
Ï߶ÎACËùÔÚÖ±ÏßµÄ
½âÎöʽΪ£ºy=2x+2£¬Ï߶ÎEFËùÔÚÖ±Ïß¹ýÔµãÇÒÓë
Ï߶ÎACËùÔÚÖ±ÏßƽÐУ¬´Ó¶ø¿ÉµÃÏ߶ÎEFËùÔÚÖ±ÏßµÄ
½âÎöʽΪ£ºy=2x£»£¨13·Ö£©
Ï߶ÎAFËùÔÚÖ±ÏßÓëÖ±ÏßCHƽÐУ¬
ÉèÖ±ÏßAFµÄ½âÎöʽΪ£ºy=-
x+m£¬
°ÑA£¨-1£¬0£©×ø±ê´úÈ룬ÇóµÃm=-
£¬
¡àÖ±ÏßAFΪ£ºy=-
x-
£®
¡ßµãEÊÇÖ±ÏßCHÓëÖ±ÏßEFµÄ½»µã£»
µãFÊÇÖ±ÏßAFÓëÖ±ÏßEFµÄ½»µã£¬
¡àµÃÏÂÃæÁ½¸ö·½³Ì×飺
ºÍ
£¬
½âµÃE£¨
£¬
£©£¬F£¨-
£¬-
£©£®£¨14·Ö£©
¡à¾ØÐεÄδ֪¶¥µãΪ£¨-1£¬2£©»ò£¨
£¬
£©¡¢£¨-
£¬-
£©£®

y=a£¨x+1£©£¨x-2£©£¬£¨1·Ö£©
°ÑµãC£¨0£¬2£©×ø±ê´úÈëÆäÖУ¬ÇóµÃa=-1£¬
y=-£¨x+1£©£¨x-2£©=-x2+x+2=-£¨x-
1 |
2 |
9 |
4 |
¡àÕâ¸ö¶þ´Îº¯ÊýµÄ½âÎöʽΪ£º
y=-x2+x+2£¨3·Ö£©
¶¥µãMµÄ×ø±êΪM£¨
1 |
2 |
9 |
4 |
[Ò²¿ÉÉèΪһ°ãʽy=ax2+bx+c£¬°ÑA¡¢B¡¢CÈýµã×ø±ê´úÈë½â³ö]
£¨2£©ÉèÏ߶ÎBMËùÔÚÖ±ÏߵĽâÎöʽΪ£ºy=kx+b£¬£¨5·Ö£©
·Ö±ð°ÑB£¨2£¬0£©¡¢M£¨
1 |
2 |
9 |
4 |
½âµÃk=-
3 |
2 |
¡ày=-
3 |
2 |
ÈôNµÄ×ø±êΪ£¨x£¬t£©£¬ÔòµÃt=-
3 |
2 |
½âµÃx=2-
2 |
3 |
ÓÉͼÐοÉÖª£ºs=S¡÷AOC+SÌÝÐÎOQNC£¨7·Ö£©
=
1 |
2 |
1 |
2 |
2 |
3 |
»¯¼òÕûÀíµÃs=-
1 |
3 |
1 |
3 |
ÆäÖÐ0£¼t£¼
9 |
4 |
£¨3£©ÒÔµãO¡¢µãA£¨»òµãO¡¢µãC£©Îª¾ØÐεÄÁ½¸ö¶¥µã£¬
µÚÈý¸ö¶¥µãÂäÔÚ¾ØÐÎÕâÒ»±ßOA£¨»ò±ßOC£©µÄ¶Ô±ßÉÏ£¬
ÈçÏÂͼ1£¬´ËʱÒ×µÃδ֪¶¥µã×ø±êÊǵãD£¨-1£¬2£©£»£¨10·Ö£©
ÒÔµãA¡¢µãCΪ¾ØÐεÄÁ½¸ö¶¥µã£¬µÚÈý¸ö¶¥µã£¨¼´µãO£©
ÂäÔÚ¾ØÐÎÕâÒ»±ßACµÄ¶Ô±ßÉÏ£¬ÈçÏÂͼ2£¬´Ëʱ
δ֪¶¥µã·Ö±ðΪµãE¡¢µãF£®£¨11·Ö£©
ËüÃǵÄ×ø±êÇó½âÈçÏ£º
¡ßACEFΪ¾ØÐΣ¬
¡à¡ÏACEΪֱ½Ç£¬ÑÓ³¤CE½»xÖáÓÚµãH£¬
ÔòÒ×µÃRt¡÷HOC¡×Rt¡÷COA£¬
¡à
OH |
OC |
OC |
OA |
¡àµãHµÄ×ø±êH£¨4£¬0£©£®¿ÉÇóµÃÏ߶ÎCHËùÔÚÖ±ÏßµÄ
½âÎöʽΪ£ºy=-
1 |
2 |
Ï߶ÎACËùÔÚÖ±ÏßµÄ
½âÎöʽΪ£ºy=2x+2£¬Ï߶ÎEFËùÔÚÖ±Ïß¹ýÔµãÇÒÓë
Ï߶ÎACËùÔÚÖ±ÏßƽÐУ¬´Ó¶ø¿ÉµÃÏ߶ÎEFËùÔÚÖ±ÏßµÄ
½âÎöʽΪ£ºy=2x£»£¨13·Ö£©
Ï߶ÎAFËùÔÚÖ±ÏßÓëÖ±ÏßCHƽÐУ¬
ÉèÖ±ÏßAFµÄ½âÎöʽΪ£ºy=-
1 |
2 |
°ÑA£¨-1£¬0£©×ø±ê´úÈ룬ÇóµÃm=-
1 |
2 |
¡àÖ±ÏßAFΪ£ºy=-
1 |
2 |
1 |
2 |
¡ßµãEÊÇÖ±ÏßCHÓëÖ±ÏßEFµÄ½»µã£»
µãFÊÇÖ±ÏßAFÓëÖ±ÏßEFµÄ½»µã£¬
¡àµÃÏÂÃæÁ½¸ö·½³Ì×飺
|
|
½âµÃE£¨
4 |
5 |
8 |
5 |
1 |
5 |
2 |
5 |
¡à¾ØÐεÄδ֪¶¥µãΪ£¨-1£¬2£©»ò£¨
4 |
5 |
8 |
5 |
1 |
5 |
2 |
5 |

µãÆÀ£º±¾ÌâÖ÷Òª¿¼²éÁË´ý¶¨ÏµÊý·¨Çóº¯ÊýµÄ½âÎöʽ£¬ÒÔ¼°Ö±ÏßƽÐÐʱ½âÎöʽ֮¼äµÄ¹Øϵ£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿