Question

1£®Èçͼ£¬Å×ÎïÏßy=-$\frac{1}{2}$x²+mx+2ÓëxÖá½»ÓÚA¡¢BÁ½µã£¬ÓëyÖá½»ÓÚµãC£¬Å×ÎïÏߵĶԳÆÖáÖ±Ïßx=$\frac{3}{2}$½»xÖáÓÚµãD£®
£¨1£©ÇómµÄÖµ£»
£¨2£©ÔÚÅ×ÎïÏߵĶԳÆÖáÉÏÕÒ³öµãP£¬Ê¹¡÷PCDÊÇÒÔCDΪÑüµÄµÈÑüÈý½ÇÐΣ¬Ö±½Óд³öPµãµÄ×ø±ê£»
£¨3£©µãEÊÇÏ߶ÎBCÉϵÄÒ»¸ö¶¯µã£¬¹ýµãE×÷xÖáµÄ´¹ÏßÓëÅ×ÎïÏßÏཻÓÚµãF£¬ÓëxÖáÏཻÓÚµãH£¬Á¬½ÓCF¡¢BF¡¢OE£¬µ±ËıßÐÎCDBFµÄÃæ»ý×î´óʱ£¬ÇëÄã˵Ã÷ËıßÐÎOCFEµÄÐÎ×´£®

Answer 1

·ÖÎö £¨1£©¸ù¾Ý¶Ô³ÆÖṫʽ£¬¿ÉµÃMµÄÖµ£»
£¨2£©¸ù¾ÝµÈÑüÈý½ÇÐεĶ¨Ò壬¿ÉµÃPµã×ø±ê£»
£¨3£©¸ù¾ÝƽÐÐÓÚyÖáµÄÖ±ÏßÉÏÁ½µã¼äµÄ¾àÀëÊǽϴóµÄ×Ý×ø±ê¼õ½ÏСµÄ×Ý×ø±ê£¬¿ÉµÃEFµÄ³¤£¬¸ù¾ÝÈý½ÇÐεÄÃæ»ý¹«Ê½£¬¿ÉµÃ¶þ´Îº¯Êý£¬¸ù¾Ý¶þ´Îº¯ÊýµÄÐÔÖÊ£¬¿ÉµÃnµÄÖµ£¬¸ù¾ÝƽÐÐËıßÐεÄÅж¨£¬¿ÉµÃ´ð°¸£®

½â´ð ½â£º£¨1£©¡ß¶Ô³ÆÖáÊÇÖ±Ïßx=$\frac{3}{2}$£¬
¡à-$\frac{m}{2¡Á£¨-\frac{1}{2}£©}$=$\frac{3}{2}$£¬
¡àm=$\frac{3}{2}$£»
£¨2£©Óɹ´¹É¶¨Àí£¬µÃ
CD=$\frac{5}{2}$£¬µ±CD=DP=$\frac{5}{2}$ʱ£¬P£¨$\frac{3}{2}$£¬$\frac{5}{2}$£©£¬£¨$\frac{3}{2}$£¬-$\frac{5}{2}$£©£¬
µ±CD=CPʱ£¬ÉèPµã×ø±êΪ£¨$\frac{3}{2}$£¬b£©£¬
¡à$\sqrt{£¨\frac{3}{2}£©^{2}+£¨b-2£©^{2}}$=$\frac{5}{2}$£¬
½âµÃb=4£¬P£¨$\frac{3}{2}$£¬4£©£¬
×ÛÉÏËùÊö£ºP₁£¨$\frac{3}{2}$£¬$\frac{5}{2}$£©£¬P₂£¨$\frac{3}{2}$£¬-$\frac{5}{2}$£©£¬P₃£¨$\frac{3}{2}$£¬4£©£»
£¨3£©ËıßÐÎOCFEÊÇƽÐÐËıßÐΣ¬
ÓÉÅ×ÎïÏßy=-$\frac{1}{2}$x²+$\frac{3}{2}$x+2£¬
Áîy=0£¬-$\frac{1}{2}$x²+$\frac{3}{2}$x+2=0£¬½âµÃx₁=-1£¬x₂=4£¬
¡àB£¨4£¬0£©£¬A£¨-1£¬0£©£¬
µ±x=0ʱ£¬y=2£¬¼´C£¨0£¬2£©£¬
ÉèBCµÄ½âÎöʽΪy=kx+b£¬°ÑB£¨4£¬0£©£¬C£¨0£¬2£©´úÈ룬µÃ
$\left\{\begin{array}{l}{4k+b=0}\\{b=2}\end{array}\right.$£¬½âµÃ$\left\{\begin{array}{l}{k=-\frac{1}{2}}\\{b=2}\end{array}\right.$£¬
Ö±ÏßBC½âÎöʽΪy=-$\frac{1}{2}$x+2£®
µãFÔÚÅ×ÎïÏßÉÏ£¬ÉèFµÄ×ø±êΪ£¨n£¬-$\frac{1}{2}$n²+$\frac{3}{2}$n+2£©£¬
µãEÔÚBCÉÏ£¬EµãµÄ×ø±êΪ£¨n£¬-$\frac{1}{2}$n+2£©£¬
EF=FH-EH=-$\frac{1}{2}$n²+2n£¬
¡ßS_{ËıßÐÎCDBF}=S_¡÷CDB+S_CFB£¬
S_CDB=$\frac{1}{2}$BD•CO=$\frac{1}{2}$¡Á£¨4-1.5£©¡Á2=$\frac{5}{2}$£¬S_CFB=$\frac{1}{2}$EF•OB•OB=$\frac{1}{2}$¡Á4¡Á£¨-$\frac{1}{2}$n²+2n£©=-n²+4n£¬
S_{ËıßÐÎCDBF}=-n²+4n+$\frac{5}{2}$=-£¨n-2£©²+$\frac{13}{2}$£¬
µ±n=2ʱ£¬ËıßÐÎCDBFµÄÃæ»ý×î´ó£¬´ËʱEF=-$\frac{1}{2}$n²+2n=2£¬EH=-$\frac{1}{2}$n+2=1£¬OH=2£¬OE=$\sqrt{O{H}^{2}+E{H}^{2}}$=$\sqrt{5}$£®
¡ßOC=EF=2£¬OC¡ÎEF£¬
¡àËıßÐÎOCFEÊÇƽÐÐËıßÐΣ®

µãÆÀ ±¾Ì⿼²éÁ˶þ´Îº¯Êý×ÛºÏÌ⣬ÀûÓõÈÑüÈý½ÇÐεĶ¨ÒåµÃ³öCD=DP£¬CD=CPÊǽâÌâ¹Ø¼ü£»ÀûÓÃÃæ»ýµÄºÍ²îµÃ³ö¶þ´Îº¯ÊýÊǽâÌâ¹Ø¼ü£¬ÓÖÀûÓÃÁËƽÐÐËıßÐεÄÅж¨£®