初三数学最大值最小值和顶点坐标公式
\u521d\u4e09\u6570\u5b66\u4e8c\u6b21\u51fd\u6570\u7684\u516c\u5f0f\uff0c\u9876\u70b9\u5750\u6807\uff0c\u5bf9\u79f0\u8f74\u5f00\u53e3\u65b9\u5411\u6027\u8d28\u4e00\u3001 \u4e8c\u6b21\u51fd\u6570\u4e00\u822c\u5f0f\uff1ay=ax²+bx+c
\u4e8c\u3001 \u6c42\u5bf9\u79f0\u8f74\u516c\u5f0f\uff1aX=-\uff08b/2a\uff09
\u4e09\u3001 \u6c42\u89e3\u6790\u5f0f\u5e38\u7528\u7684\uff1a
1.\u4ea4\u70b9\u5f0f y=a(x-x1)(x-x2) [\u4ec5\u9650\u4e8e\u4e0ex\u8f74\u6709\u4ea4\u70b9A\uff08x1\uff0c0\uff09\u548c B\uff08x2\uff0c0\uff09\u7684\u629b\u7269\u7ebf]
2. \u9876\u70b9\u5f0f y=a(x+h)²+k \u5b83\u7684\u9876\u70b9\u662f(-h,k)
\u56db\u3001 \u6c42\u6839 \u5982\u56fe
\u4e94\u3001\u5173\u4e8e\u4e0ex\u8f74\u7684\u4ea4\u70b9 \u5229\u7528 \u0394=b^2-4ac,
\u0394\uff1e0\uff0c\u56fe\u8c61\u4e0ex\u8f74\u4ea4\u4e8e\u4e24\u70b9\uff1a
\uff08[-b-\u221a\u0394]/2a\uff0c0\uff09\u548c\uff08[-b+\u221a\u0394]/2a\uff0c0\uff09\uff1b
\u0394\uff1d0\uff0c\u56fe\u8c61\u4e0ex\u8f74\u4ea4\u4e8e\u4e00\u70b9\uff1a
\uff08-b/2a\uff0c0\uff09\uff1b
\u0394\uff1c0\uff0c\u56fe\u8c61\u4e0ex\u8f74\u65e0\u4ea4\u70b9\uff1b
\u516d \u5355\u8c03\u6027\uff08\u589e\u51cf\u6027\uff09
a\uff1e0 \u65f6 \u5f00\u53e3\u5411\u4e0a \u5bf9\u79f0\u8f74\u5de6\u8fb9\u5355\u8c03\u9012\u51cf \u5bf9\u79f0\u8f74\u53f3\u8fb9\u9012\u589e
a\uff1c0 \u65f6 \u5f00\u53e3\u5411\u4e0b \u5bf9\u79f0\u8f74\u5de6\u8fb9\u5355\u8c03\u9012\u589e \u5bf9\u79f0\u8f74\u53f3\u8fb9\u9012\u51cf
\u6700\u5927\u503c\u51fd\u6570\uff1aMAX\u8bed\u6cd5\uff1aMAX(number1,number2,...)\u6ce8\u91ca\uff1a1\u3001\u5176\u4e2d\u7684\u53c2\u6570number1\u3001number2\u7b49\u53ef\u4ee5\u662f\u6570\u5b57\uff0c\u5355\u5143\u683c\u540d\u79f0\uff0c\u8fde\u7eed\u5355\u5143\u683c\u533a\u57df\uff0c\u903b\u8f91\u503c\uff1b2\u3001\u82e5\u662f\u5355\u5143\u683c\u540d\u79f0\u3001\u8fde\u7eed\u5355\u5143\u683c\u533a\u57df\u7b49\u6570\u636e\u5f15\u7528\uff0c\u901a\u5e38\u53ea\u8ba1\u7b97\u5176\u4e2d\u7684\u6570\u503c\u6216\u901a\u8fc7\u516c\u5f0f\u8ba1\u7b97\u7684\u6570\u503c\u90e8\u5206\uff0c\u4e0d\u8ba1\u7b97\u903b\u8f91\u503c\u548c\u5176\u5b83\u5185\u5bb9\uff1b3\u3001\u5982\u679cmax\u51fd\u6570\u540e\u9762\u7684\u53c2\u6570\u6ca1\u6709\u6570\u5b57\uff0c\u4f1a\u8fd4\u56de0\u793a\u4f8b\uff1a\u5982\u679c A1:A5 \u5305\u542b\u6570\u5b57 10\u30017\u30019\u300127 \u548c 2\uff0c\u5219\uff1aMAX(A1:A5) \u7b49\u4e8e 27MAX(A1:A5,30) \u7b49\u4e8e 30
\u6700\u5c0f\u503c\u51fd\u6570\uff1aMINMIN(number1, number2, ...)\u6ce8\u91ca\uff1a1\u3001\u5176\u4e2d\u7684\u53c2\u6570number1\u3001number2\u7b49\u53ef\u4ee5\u662f\u6570\u5b57\uff0c\u5355\u5143\u683c\u540d\u79f0\uff0c\u8fde\u7eed\u5355\u5143\u683c\u533a\u57df\uff0c\u903b\u8f91\u503c\uff1b2\u3001\u82e5\u662f\u5355\u5143\u683c\u540d\u79f0\u3001\u8fde\u7eed\u5355\u5143\u683c\u533a\u57df\u7b49\u6570\u636e\u5f15\u7528\uff0c\u901a\u5e38\u53ea\u8ba1\u7b97\u5176\u4e2d\u7684\u6570\u503c\u6216\u901a\u8fc7\u516c\u5f0f\u8ba1\u7b97\u7684\u6570\u503c\u90e8\u5206\uff0c\u4e0d\u8ba1\u7b97\u903b\u8f91\u503c\u548c\u5176\u5b83\u5185\u5bb9\uff1b3\u3001\u5982\u679cmin\u51fd\u6570\u540e\u9762\u7684\u53c2\u6570\u6ca1\u6709\u6570\u5b57\uff0c\u4f1a\u8fd4\u56de0\u793a\u4f8b\uff1aA1:A5 \u4e2d\u4f9d\u6b21\u5305\u542b\u6570\u503c 10\uff0c7\uff0c3\uff0c27 \u548c 2\uff0c\u90a3\u4e48MIN(A1:A5) \u7b49\u4e8e 2MIN(A1:A5, 0) \u7b49\u4e8e 0
X=﹣b/2a Y=﹣b±√b�0�5-4ac/2a
绛旓細a澶т簬0 寮鍙ｅ悜涓 鏈鏈灏忓 a灏忎簬0 寮鍙ｅ悜涓 鏈鏈澶у 鏈鍊鍏紡鏄痽=(b骞虫柟-4ac)/4a 椤剁偣鍧愭爣鍏紡 (2a/b,(b骞虫柟-4ac)/4a)
绛旓細y=-1/3(x-1/2)²+49/4 鈭椤剁偣鍧愭爣锛1/2,49/4锛夊绉拌酱x=1/2 鏈鏈澶у49/4
绛旓細姹備簩娆″嚱鏁鏈澶э紙灏忥級鍊鐨勪竴鑸柟娉曟槸鍒╃敤鈥滈厤鏂规硶鈥濆皢浜屾鍑芥暟鍖栨垚椤剁偣寮忥紝鐒跺悗鏍规嵁浜屾鍑芥暟鐨椤剁偣鍧愭爣鍙互鍒ゆ柇鍑轰簩娆″嚱鏁扮殑鏈澶у煎拰鏈灏忓銆傚叿浣撴楠ゅ涓嬶細瀵逛簬浜屾鍑芥暟 f(x) = ax^2 + bx + c锛屽彲浠ュ皢鍏跺寲鎴愰《鐐瑰紡锛歠(x) = a(x - h)^2 + k 鍏朵腑锛(h, k) 涓轰簩娆″嚱鏁扮殑椤剁偣鍧愭爣...
绛旓細鍒嗘瀽锛氫簩娆″嚱鏁颁腑锛屼簩娆￠」绯绘暟a鍐冲畾浜嗗紑鍙ｆ柟鍚戯紝鍗砤>0锛屽紑鍙ｅ悜涓婏紝鍑芥暟鏈鏈灏忓锛沘<0,寮鍙ｅ悜涓嬶紝鍑芥暟鏈鏈澶у銆備篃鍙互閫氳繃浣滃浘鐢诲嚭鎶涚墿绾匡紝鏇村姞鐩磋銆傞涔犵粌涔 鍑芥暟y=-2(x-1)² 椤剁偣鍧愭爣鍜屽绉拌酱 鍒嗘瀽锛氬洜涓轰簩娆￠」绯绘暟涓-2锛屽皬浜0锛屽紑鍙ｅ悜涓嬶紝璇存槑鍑芥暟鏈夋渶澶у硷紝褰搙=1(鍗充簩娆″嚱鏁板...
绛旓細瀵逛簬浜屾鍑芥暟y=ax^2+bx+c锛椤剁偣灏卞湪鍏跺绉拌酱涓娿傚绉拌酱鏂圭▼涓簒=-b/2a锛屾墍浠ラ《鐐规í鍧愭爣涓-b/2a锛屼唬鍏ュ嚱鏁板悗鍙眰寰楃旱鍧愭爣y銆傛渶缁堥《鐐瑰潗鏍囦负(-b/2a,(4ac-b²)/4a)
绛旓細浜屾鍑芥暟鐨鏈澶у煎拰鏈灏忓鍙互閫氳繃璁＄畻鎶涚墿绾跨殑椤剁偣鏉ュ緱鍒般傛姏鐗╃嚎鐨椤剁偣鍧愭爣涓 (-b/2a, f(-b/2a))锛屽叾涓 f(x) 琛ㄧず浜屾鍑芥暟鐨勫笺傛墍浠ワ紝褰 a > 0 鏃讹紝鏈灏忓间负 f(-b/2a)锛屽綋 a < 0 鏃讹紝鏈澶у间负 f(-b/2a)銆傞渶瑕佹敞鎰忕殑鏄紝濡傛灉浜屾鍑芥暟鐨勭郴鏁 a 鐨勭粷瀵瑰奸潪甯稿皬锛屽彲鑳藉湪璁＄畻...
绛旓細鎶涚墿绾挎槸浜屾鍑芥暟鐨勫浘鍍忥紝鍏锋湁鐗瑰畾鐨勫舰鐘躲傚湪鏁板涓紝鎶涚墿绾跨殑鏈澶у鎴鏈灏忓鍙互閫氳繃姹傝В鎶涚墿绾挎墍瀵瑰簲鐨勪簩娆″嚱鏁扮殑椤剁偣鏉ュ緱鍒般傛姏鐗╃嚎涓鑸彲琛ㄧず涓轰簩娆″嚱鏁扮殑鏍囧噯寮忥細y=ax^2+bx+c锛屽叾涓璦銆乥銆乧涓哄父鏁帮紝a涓嶇瓑浜0銆傞《鐐圭殑妯鍧愭爣鍙敱x = -b/(2a)姹傚緱銆(2) 鐭ヨ瘑鐐硅繍鐢細姹傛姏鐗╃嚎鐨勬渶澶у兼垨鏈...
绛旓細锛1锛夊紑鍙ｆ柟鍚:鍚戜笂 锛2锛椤剁偣鍧愭爣锛氾紙1/2锛7/4锛夊绉拌酱锛氱洿绾縓=1/2 锛3锛鏈灏忓锛7/4 锛4锛夋姏鐗╃嚎鍜寈杞翠笉鐩镐氦锛屽拰y杞翠氦涓庯紙0锛2锛夛紙5锛夊嚱鏁扮殑鍥惧儚锛氱暐 锛6锛夊綋x涓轰换浣曞奸兘y>0 锛7锛墄>1/2 鏃讹紝y闅弜鐨勫澶ц屽澶 x<1/2 鏃讹紝y闅弜鐨勫澶ц屽噺灏 ...
绛旓細鎶涚墿绾跨殑鏈澶у间笌鏈灏忓鐨勬眰娉曟槸锛氭眰鍑椤剁偣鐨鍧愭爣锛岄《鐐圭殑绾靛潗鏍囧氨鏄渶澶у兼垨鏈灏忓笺傦紙1锛夊綋鎶涚墿绾跨殑寮鍙ｅ悜涓嬶紙鎴栬В鏋愬紡涓簩娆￠」绯绘暟涓鸿礋锛夋椂,椤剁偣鐨勭旱鍧愭爣灏辨槸鏈澶у笺傦紙2锛夊綋鎶涚墿绾跨殑寮鍙ｅ悜涓婏紙鎴栬В鏋愬紡涓簩娆￠」绯绘暟涓烘锛夋椂,椤剁偣鐨勭旱鍧愭爣灏辨槸鏈灏忓笺傝锛歽=ax^2+bx+c y = ax^2+...
绛旓細鍥炵瓟锛氭寜鐓ч璁,鎴戜滑鏈缁堥渶瑕佸皢涓嬪垪鏂圭▼鍙樻崲鎴恲=a(x-b)^2+c鐨勫舰寮忋傛墍浠,瀵逛簬涓嬭堪鏂圭▼,绗竴姝ユ垜浠渶瑕佸皢a纭畾骞舵彁鍙栧嚭鏉,鑰屽悗纭畾b鐨勬暟鍊,鏈鍚庢槸c鐨勭‘瀹氥 x=b鍗充负瀵圭О杞,鑰(b,c)鍗充负椤剁偣鍧愭爣銆傝嫢a澶т簬0,鍒欐姏鐗╃嚎寮鍙ｅ悜涓,瀛樺湪鏈灏忓,鍗抽《鐐瑰潗鏍囧搴旂殑y鍊笺傝嫢a灏忎簬0,鍒欐姏鐗╃嚎寮鍙ｅ悜涓,瀛樺湪...
