Question

13£®Èçͼ£¬ÒÑÖª¶þ´Îº¯Êýy=-$\frac{1}{2}$x²+bx+cµÄͼÏó¾­¹ý£¨1£¬0£©£¬B£¨0£¬-6£©Á½µã£¬
£¨1£©ÇóÕâ¸ö¶þ´Îº¯Êý½âÎöʽ£»
£¨2£©Éè¸Ã¶þ´Îº¯ÊýͼÏóÓëxÖá½»ÓÚµãC£¬Á¬½ÓBA¡¢BC£¬Çó¡÷ABCµÄÃæ»ý£»
£¨3£©¸ù¾ÝͼÏó£¬Ð´³öº¯ÊýÖµyΪ¸ºÊýʱ£¬×Ô±äÁ¿xµÄÈ¡Öµ·¶Î§£»
£¨4£©Ìî¿Õ£ºÒªÊ¹¸Ã¶þ´Îº¯ÊýµÄͼÏóÓëxÖáÖ»ÓÐÒ»¸ö½»µã£¬Ó¦¸Ã°ÑͼÏóÑØyÖáÏòÏÂƽÒÆ$\frac{121}{8}$¸öµ¥Î»£®

Answer 1

·ÖÎö £¨1£©ÀûÓôý¶¨ÏµÊý·¨£¬½«£¨1£¬0£©¡¢B£¨0£¬-6£©´úÈëy=-$\frac{1}{2}$x²+bc+c¼´¿ÉÇó³öº¯Êý½âÎöʽ£»
£¨2£©¸ù¾Ý½âÎöʽ£¬Çó³öCµã×ø±ê£¬ÔÙÀûÓÃÈý½ÇÐÎÃæ»ý¹«Ê½¼´¿ÉÇó³ö¡÷ABCµÄÃæ»ý£»
£¨3£©¸ù¾ÝÅ×ÎïÏßÓëxÖáµÄ½»µã×ø±ê£¬¼´¿ÉµÃ³öxµÄÈ¡Öµ·¶Î§£»
£¨4£©Çó³öÅ×ÎïÏߵĶ¥µã×Ý×ø±ê£¬¼´¿É¸ù¾ÝƽÒÆ֪ʶµÃ³ö´ð°¸£®

½â´ð ½â£º£¨1£©°Ñ£¨1£¬0£©¡¢B£¨0£¬-6£©´úÈëy=-$\frac{1}{2}$x²+bx+c£¬µÃ£º$\left\{\begin{array}{l}{-\frac{1}{2}+b+c=0}\\{c=-6}\end{array}\right.$£¬
½âµÃ$\left\{\begin{array}{l}{b=\frac{13}{2}}\\{c=-6}\end{array}\right.$£®
¹ÊÕâ¸ö¶þ´Îº¯ÊýµÄ½âÎöʽΪy=-$\frac{1}{2}$x²+$\frac{13}{2}$x-6£»

£¨2£©¡ß¸ÃÅ×ÎïÏ߶ԳÆÖáΪֱÏßx=-$\frac{\frac{13}{2}}{2¡Á£¨-\frac{1}{2}£©}$=$\frac{13}{2}$£¬
¡àµãCµÄ×ø±êΪ£¨12£¬0£©£¬
¡àAC=OC-OA=12-1=11£¬
¡àS_¡÷ABC=$\frac{1}{2}$¡ÁAC¡ÁOB=$\frac{1}{2}$¡Á11¡Á6=33£»

£¨3£©ÓÉͼ¿ÉÖª£¬º¯ÊýÖµyΪ¸ºÊýʱ£¬×Ô±äÁ¿xµÄÈ¡Öµ·¶Î§Îªx£¼1»òx£¾12£®

£¨4£©½«£¨2£©ÖÐËùÇóx=$\frac{13}{2}$´úÈë½âÎöʽ£¬¼´¿ÉµÃ¶¥µã×Ý×ø±êΪ-$\frac{1}{2}$¡Á£¨$\frac{13}{2}$£©²+$\frac{13}{2}$¡Á$\frac{13}{2}$-6=$\frac{121}{8}$£¬
¿É¼û°ÑͼÏóÑØyÖáÏòÏÂƽÒÆ$\frac{121}{8}$¸öµ¥Î»£¬Ôò¸Ã¶þ´Îº¯ÊýµÄͼÏóÓëxÖáÖ»ÓÐÒ»¸ö½»µã£®
¹Ê´ð°¸Îª£º$\frac{121}{8}$£®

µãÆÀ ´ËÌâ×ÛºÏÐÔ½ÏÇ¿£¬¿¼²éÁËÅ×ÎïÏßÓëxÖáµÄ½»µã¡¢Óôý¶¨ÏµÊý·¨Çóº¯Êý½âÎöʽ¡¢¶þ´Îº¯ÊýͼÏóÓ뼸ºÎ±ä»»µÈ֪ʶ£¬½â´ðʱҪÀíÇå˼·£¬²¢×¢Òâ¼ÆËãµÄÕýÈ·ÐÔ£®