如图，抛物线y=ax2+bx+c的对称轴为直线x=1，与x轴交于A、B两点，与y轴交于点C，其中A（-1，0）、C（0，3 如图，抛物线y=ax 2 +bx+c的对称轴为直线x=1，与...

\u5982\u56fe,\u629b\u7269\u7ebfy=ax²+bx+c\u7684\u5bf9\u79f0\u8f74\u4e3a\u76f4\u7ebfx=1,\u4e0ex\u8f74\u4ea4\u4e0eA,B\u4e24\u70b9,\u4e0ey\u8f74\u4ea4\u4e0e\u70b9C,\u5176\u4e2dA(-1,0),C(0,3)

\u89e3\uff1a\u56e0\u4e3a\u629b\u7269y=ax^2+bx+c\u7684\u5bf9\u79f0\u8f74\u4e3a\u76f4\u7ebfx=1
\u6240\u4ee5\u70b9B(3.0)
\u628a\u70b9A(-1\uff0c0) B(3\uff0c0) C(0\uff0c3)\u5206\u522b\u4ee3\u5165y=ax^2+bx+c\u5f97\u65b9\u7a0b\u7ec4\uff1a
0=a-b+c
0=9a+3b+c
3=0+0+c
\u89e3\u65b9\u7a0b\u7ec4\u5f97\uff1a
a=-1
b=2
c=3
\u628aa=-1 b=2 c=3\u4ee3\u5165y=ax^2+bx+c\u5f97\uff1a
y=-x^2+2x+3

\u89e3\uff1a\uff081\uff09\u7531\u9898\u610f\u5f97 \uff0c\u6240\u4ee5\uff0c\u6b64\u629b\u7269\u7ebf\u7684\u89e3\u6790\u5f0f\u4e3a \u3002 \uff082\uff09\u2460\u5982\u56fe\uff0c\u9876\u70b9P\u4e3a\uff081\uff0c4\uff09\uff0cCP \uff0cBP \uff0c\u53c8\u56e0\u4e3a \uff0c\u6240\u4ee5\u2220PCB=90\u00b0\uff0c\u53c8\u56e0\u4e3aO\u2032C\u2032 \u2225CP\uff0c\u6240\u4ee5O\u2032C\u2032\u22a5BC\uff0c\u6240\u4ee5\u70b9O\u2032\u5728BC\u4e0a\uff0c\u6240\u4ee5\u03b1=45\u00b0\uff1b\u2461\u5982\u5907\u7528\u56fe1\uff0c\u5f53BC\u2032\u4e0eBP\u91cd\u5408\u65f6\uff0c\u8fc7\u70b9O\u2032\u4f5cO\u2032D\u22a5OB\u4e8eD\uff0c\u56e0\u4e3a\u2220PBC+\u2220CBO\u2032=\u2220CBO\u2032+\u2220ABO\u2032=45\u00b0\uff0c\u6240\u4ee5\u2220ABO\u2032=\u2220PBC\uff0c\u5219\u25b3DBO\u2032\u223d\u25b3CBP\uff0c\u6240\u4ee5 \uff0c\u6240\u4ee5BD=3O\u2032D\uff0c\u8bbeO\u2032D= x\uff0c\u5219BD=3x\uff0c\u6839\u636e\u52fe\u80a1\u5b9a\u7406\uff0c\u5f97 \uff0c\u6240\u4ee5BD \uff0c\u6240\u4ee5\u70b9O\u2032\u7684\u5750\u6807\u4e3a \u3002\u5982\u5907\u7528\u56fe2\uff0c\u5f53BO\u2032\u4e0eBP\u91cd\u5408\u65f6\uff0c\u8fc7\u70b9B\u4f5cx\u8f74\u7684\u5782\u7ebfBE\uff0c\u8fc7\u70b9C\u2032\u4f5cC\u2032E\u22a5BE\u4e8eE\uff0c\u56e0\u4e3a\u2220PBE+\u2220EBC\u2032=\u2220PBE+\u2220CBP=45\u00b0\uff0c\u6240\u4ee5\u2220EBC\u2032=\u2220PBC\uff0c\u6240\u4ee5\u25b3EBC\u2032\u223d\u25b3CBP\uff0c\u6240\u4ee5 \uff0c\u6240\u4ee5BE=3C\u2032E\uff0c\u8bbeC\u2032E\u4e3ay\uff0c\u5219BE=3y\uff0c\u6839\u636e\u52fe\u80a1\u5b9a\u7406\uff0c\u5f97 \uff0c\u6240\u4ee5BE \uff0c\u6240\u4ee5C\u2032\u7684\u5750\u6807\u4e3a \u3002

（1）由题意得

濡傚浘,鎶涚墿绾縴=ax^2+bx+8(a鈮0)涓巟杞翠氦浜庣偣A(-2,0),鐐笲涓巠杞翠氦浜庣偣C... 绛旓細绛旓細1锛夌涓闂凡瑙ｇ瓟寰楀嚭y=-x^2+2x+8 2锛夌偣A锛-2,0锛夛紝B锛4,0锛夛紝C锛0,8锛夛紝D锛1,9锛塐N鐩寸嚎鎶婁笁瑙掑舰BOC鐨勯潰绉垎鎴愪袱鍗婏紝鍒橭N涓嶣C鐨勪氦鐐瑰氨鏄疊C鐨勪腑鐐 BC涓偣P锛2,4锛夋墍浠ワ細鐩寸嚎ON涓簓=2x 浠ｅ叆鎶涚墿绾鏂圭▼寰楋細y=2x=-x^2+2x+8 x^2=8 瑙ｅ緱锛歺=-2鈭2鎴栬厁=2鈭2 鎵浠ワ細鐐筃... 宸茬煡鎶涚墿绾縴=ax2+bx+c鐨勫浘璞濡傚浘,鍒欎笅鍒楃粨璁:鈶燼bc>0;鈶+b+c=2;鈶... 绛旓細鈶犫埖鎶涚墿绾鐨勫紑鍙ｅ悜涓婏紝鈭碼锛0锛屸埖涓y杞寸殑浜ょ偣涓哄湪y杞寸殑璐熷崐杞翠笂锛屸埓c锛0锛屸埖瀵圭О杞翠负x=?b2a锛0锛屸埓a銆乥鍚屽彿锛屽嵆b锛0锛屸埓abc锛0锛屾晠鈶犻敊璇紱鈶″綋x=1鏃讹紝鍑芥暟鍊间负2锛0锛屸埓鈶+b+c=2瀵瑰綋x=-1鏃讹紝鍑芥暟鍊=0锛屽嵆a-b+c=0锛岋紙1锛夊張a+b+c=2锛灏哸+c=2-b浠ｅ叆锛1锛锛2-2b=... 濡傚浘,宸茬煡鎶涚墿绾縴=ax2+bx+c(a鈮0)鐨勫绉拌酱涓虹洿绾縳=1,涓旀姏鐗╃嚎缁忚繃A(-1... 绛旓細锛1锛夆埖瀵圭О杞翠负x=1锛屼笖鎶涚墿绾缁忚繃A锛-1锛0锛夛紝鈭寸偣B锛3锛0锛夛紝璁y=a锛坸-3锛夛紙x+1锛夛紝鎶奀锛0锛-3锛変唬鍏ヨВ寰楋細a=1锛屾晠瑙ｆ瀽寮忎负锛歽=x2-2x-3锛涳紙2锛夆埖OC=3锛孫B=3锛屸埓OC=OB锛屸埓鈻矪OC鏄瓑鑵扮洿瑙掍笁瑙掑舰锛屸埖鈻砅AB鈭解柍OBC锛屸埓鈻砅AB鏄瓑鑵扮洿瑙掍笁瑙掑舰锛岃瀵圭О杞翠笌x杞翠氦鐐逛负D锛屽垯DP... 濡傚浘,鎶涚墿绾縴=ax^2+bx+c涓巟杞寸殑涓涓氦鐐笰鍦ㄧ偣(-2,0)鍜(-1,0)涔嬮棿... 绛旓細1abc__锛淿__0 2椤剁偣C鏄煩褰EFG涓婏紙鍖呮嫭杈圭晫鍜屽唴閮級鐨勪竴涓姩鐐癸紝褰撻《鐐笴涓嶥鐐归噸鍚堬紝椤剁偣鍧愭爣涓猴紙1锛3锛変笖鎶涚墿绾杩囷紙-1锛0锛夛紝鍒欏畠涓巟杞寸殑鍙︿竴涓氦鐐逛负锛3锛0锛夛紝鈭翠唬鍏y=ax2+bx+c涓紝鍙互姹傚嚭a=-3/4锛涘綋椤剁偣C涓嶧鐐归噸鍚堬紝椤剁偣鍧愭爣涓猴紙3锛2锛変笖鎶涚墿绾胯繃锛-1锛0锛夛紝鍒欏畠涓巟杞寸殑... 濡傚浘,鎶涚墿绾縴=ax^2+bx+2/5杩囩偣A(1.0), B(5.0).涓庤酱鐩镐氦浜庣偣C. (1... 绛旓細(1)鎶涚墿绾縴=ax^2+bx+2/5杩囩偣A(1.0), B(5.0),鈭磞=a(x-1)(x-5),浠=0寰5a=2/5,a=2/25.鈭磞=(2/25)(x-1)(x-5)=(2/25)x^2-(12/25)x+2/5.鈶 (2)璁綞(3,m),m>0,浠锛孊锛孍, F涓洪《鐐圭殑鍥涜竟褰 鏄竟闀夸负4鐨勮彵褰,鈭碅E^2=4+m^2=16,m^2=12,m=2鈭3... 濡傚浘8,鎶涚墿绾縴 = ax2 + bx + c缁忚繃A(1,0)銆丅(5,0)涓ょ偣,鏈浣庣偣 绛旓細锛1锛夋牴鎹鎶涚墿绾縴=ax 2 +bx+c缁忚繃A锛1锛0锛夈丅锛5锛0锛変袱鐐癸紝鍙緱鍑芥暟瀵圭О杞存柟绋嬶紝鍙堝洜涓哄嚱鏁版渶浣庣偣鐨勭旱鍧愭爣涓-4锛屾墍浠ュ彲姹傜殑鎶涚墿绾块《鐐瑰潗鏍囷紝璁惧嚭鎶涚墿绾块《鐐瑰紡锛屽埄鐢ㄥ緟瀹氱郴鏁版硶瑙ｇ瓟鍗冲彲锛涳紙2锛変綔鍑鸿緟鍔╃嚎锛岃繃鐐筄 1 浣淥 1 P鈯杞翠簬P锛岃繛鎺 1 A锛屾瀯閫犳湁涓瑙掆垹AO 1 P涓庘垹ACB鐩哥瓑鐨... 濡傚浘,宸茬煡鎶涚墿绾縴=ax骞虫柟+bx+2涓巟杞翠氦浜嶢(-4,0),B(1,0)涓ょ偣,涓巠杞翠氦... 绛旓細鎶夾锛-4锛0锛塀锛1锛0锛変唬鍏鎶涚墿绾鏂圭▼寰 锝16a-4b+2=0 瑙ｅ緱锝沘=-1/2 a+b+2=0 b=-3/2 鏁y=-x^2/2-3x/2+2 鍒機锛0锛2锛夎繛鎺C锛屽垯褰揚浣嶄簬AC涓庡绉拌酱鐨勪氦鐐规椂鈻砅BC鍛ㄩ暱鏈灏忥紝鍗充负AC闀垮害锛屾槸鈭(4^2+2^2)=2鈭5 璁惧绉拌酱涓嶢C浜や簬P锛屼笌x杞翠氦浜嶲 鍒橯锛-3/2,0... 濡傚浘,宸茬煡鎶涚墿绾縴=ax^2+bx+c涓巟杞翠氦浜嶢B涓ょ偣,涓巠杞翠氦浜庣偣C,D涓篛C鐨勪腑... 绛旓細璁捐繃AD鐨勭洿绾夸负y=kx+2锛鎶奅锛2,6锛変唬鍏ュ緱y=2x+2 銆 鐩寸嚎涓巟杞寸殑浜ょ偣A鍧愭爣涓篈锛-1,0锛夈 鍥犱负鎶涚墿绾杩嘇锛孋,E锛 鎵浠ヨВ鏋愬紡涓簓=-x²+3x+4. 2,鍥犱负鎶涚墿绾跨殑瀵圭О杞翠负x=3/2锛屾墍浠锛3/2,0锛夛紝瑕佷娇鈻矨BQ鈭解柍ADF锛岄』灏咲F鍚戝彸骞崇Щ3/2涓崟浣嶏紝鎵浠锛2/3,10/3锛夈 宸茬煡濡傚浘,鎶涚墿绾縴=ax2+bx+c杩囩偣A(-1,0),涓旂粡杩囩洿绾縴=x-3涓庡潗鏍囪酱鐨勪袱... 绛旓細鎶涚墿绾鐨勮В鏋愬紡涓 y=x^2-2x-3 2銆侀厤鏂逛箣鍚庢姏鐗╃嚎涓 y=(x-1)^2-4 椤剁偣鍧愭爣涓(1,-4)3銆佸悜閲廈C=(3,3) 璁綧(x,y) 鍚戦噺OM=(x,y)鍥犱负OM鈯C锛屾墍浠3x+3y=0 鍥犱负M鍦ㄧ鍥涜薄闄愮殑鎶涚墿绾夸笂鎵浠(x,x^2-2x-3) x>0,y<0 3x+3(x^2-2x-3)=0 瑙ｅ緱M((1+鏍瑰彿涓13)/2,-(1... 濡傚浘,鍦ㄧ洿瑙掑潗鏍囩郴涓,鎶涚墿绾縴=ax^2+bx+c(a涓嶇瓑浜0)涓巟杞翠氦浜庣偣A(-1... 绛旓細y = a(x + 1)(x -3) = ax² -2ax -3a 鎶涚墿绾浜杞翠笌鐐笴锛0锛3), 3 = -3a, a = -1 y = -x² + 2x + 3 E涓虹嚎娈礝C涓婄殑涓夌瓑鍒嗙偣, E(0, 1)鎴朎(0, 2)璁綪(p, p-1) (鍦▂ = x -1涓婏級鍒橯(p, -p² + 2p + 3)(1) E(0, 1)EP=EQ, (... 扩展阅读：求解方程计算器 ... 抛物线弦长x1+x2+p ... 已知抛物线y ax2 bx c ... 二次函数y=ax2+bx+c ... ax bx+c 0 ... (x+a)(x-b)公式 ... 抛物线y2=4x ... 已知抛物线yx2+bx+c与x轴 ... 抛物线yax2十bx十c的意思 ... 本站交流只代表网友个人观点，与本站立场无关 欢迎反馈与建议，请联系电邮 2024© 车视网