{"id":28935,"date":"2021-04-27T13:00:19","date_gmt":"2021-04-27T13:00:19","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28935"},"modified":"2024-09-22T02:15:26","modified_gmt":"2024-09-22T02:15:26","slug":"%e6%8a%9b%e7%89%a9%e7%ba%bf%e5%8f%8a%e5%85%b6%e5%9b%be%e5%bd%a2%e7%9a%84%e8%a1%a8%e5%be%81","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e6%8a%9b%e7%89%a9%e7%ba%bf%e5%8f%8a%e5%85%b6%e5%9b%be%e5%bd%a2%e7%9a%84%e8%a1%a8%e5%be%81\/","title":{"rendered":"\u629b\u7269\u7ebf\u53ca\u5176\u56fe\u5f62\u7684\u8868\u5f81"},"content":{"rendered":"<p><center><\/p>\n<h1>\u629b\u7269\u7ebf\u53ca\u5176\u56fe\u5f62\u7684\u8868\u5f81<\/h1>\n<p><em><strong>\u6458\u8981:<\/strong><br \/>\n   \u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u4ece\u4e00\u822c\u65b9\u7a0b\u548c\u6807\u51c6\u5f62\u5f0f\u51fa\u53d1\uff0c\u89e3\u91ca\u5982\u4f55\u8bc6\u522b\u5173\u952e\u5143\u7d20\uff0c\u5982\u9876\u70b9\u3001\u7126\u70b9\u3001\u51c6\u7ebf\u3001\u5bf9\u79f0\u8f74\u4ee5\u53ca\u53ef\u80fd\u7684\u4e0eX\u8f74\u7684\u4ea4\u70b9\u3002<br \/>\n   <\/em><br \/>\n   <strong>\u5b66\u4e60\u76ee\u6807:<\/strong><br \/>\n   \u672c\u8282\u8bfe\u7ed3\u675f\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol style=\"text-align: left;\">\n<li><strong>\u8ba1\u7b97<\/strong>\u9876\u70b9\u3001\u7126\u70b9\u548c\u51c6\u7ebf\u7684\u4f4d\u7f6e\uff0c\u4ece\u5176\u4e00\u822c\u5f62\u5f0f\u548c\u6807\u51c6\u5f62\u5f0f\u51fa\u53d1\u3002<\/li>\n<li><strong>\u8f6c\u6362<\/strong>\u6807\u51c6\u65b9\u7a0b\u4e3a\u4e00\u822c\u5f62\u5f0f\u4ee5\u63d0\u53d6\u51e0\u4f55\u4fe1\u606f\u3002<\/li>\n<li><strong>\u7ed8\u5236<\/strong>\u4f7f\u7528\u83b7\u5f97\u7684\u4fe1\u606f\u7ed8\u5236\u629b\u7269\u7ebf\u7684\u56fe\u5f62\u3002<\/li>\n<\/ol>\n<p>   <strong>\u5185\u5bb9\u7d22\u5f15<\/strong><br \/>\n   <a href=\"#1\">\u629b\u7269\u7ebf\u7684\u4e00\u822c\u5f62\u5f0f\u548c\u6807\u51c6\u5f62\u5f0f<\/a><br \/>\n   <a href=\"#2\">\u4ece\u4e00\u822c\u65b9\u7a0b\u8868\u5f81\u629b\u7269\u7ebf<\/a><br \/>\n   <a href=\"#3\">\u4ece\u6807\u51c6\u65b9\u7a0b\u8868\u5f81\u629b\u7269\u7ebf<\/a><br \/>\n   <a href=\"#4\">\u4f7f\u7528Excel\u8fdb\u884c\u81ea\u52a8\u8868\u5f81<\/a>\n   <\/p>\n<p><\/center><br \/>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/C6DbrJDiZTM\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u629b\u7269\u7ebf\u7684\u4e00\u822c\u5f62\u5f0f\u548c\u6807\u51c6\u5f62\u5f0f<\/h2>\n<p style=\"text-align: justify;\">\u5728\u4e0a\u4e00\u8bfe\u4e2d\uff0c\u6211\u4eec\u770b\u5230\u629b\u7269\u7ebf\u53ef\u4ee5\u901a\u8fc7\u629b\u7269\u7ebf\u7684\u4e00\u822c\u65b9\u7a0b\u4ee3\u6570\u5730\u8868\u793a\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x-x_0)^2 =4f(y-y_0)<\/span>\n<p style=\"text-align: justify;\">\u5176\u4e2d\u5750\u6807\u5bf9<span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0)<\/span>\u662f\u9876\u70b9\u7684\u4f4d\u7f6e\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>\u662f\u7126\u8ddd\u3002\u5982\u679c<span class=\"katex-eq\" data-katex-display=\"false\">f \\gt 0<\/span>\uff0c\u90a3\u4e48\u7126\u70b9\u5728\u9876\u70b9\u4e4b\u4e0a<span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>\u7684\u8ddd\u79bb\uff1b\u5982\u679c<span class=\"katex-eq\" data-katex-display=\"false\">f\\lt 0<\/span>\uff0c\u5219\u7126\u70b9\u5728\u9876\u70b9\u4e4b\u4e0b<span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>\u7684\u8ddd\u79bb\u3002<\/p>\n<p style=\"text-align: justify;\">\u6211\u4eec\u8fd8\u770b\u5230\uff0c\u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\u5f62\u5f0f\u7b49\u6548\u4e8e\u4e8c\u6b21\u591a\u9879\u5f0f\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x) = ax^2 + bx + c,<\/span> \u5176\u4e2d <span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=228s\" target=\"_blank\" rel=\"noopener\"><strong>\u8868\u5f81\u629b\u7269\u7ebf<\/strong><\/a>\u5c31\u662f\u63ed\u793a\u4ee5\u4e0b\u4fe1\u606f\u3002<\/p>\n<ul style=\"text-align: justify;\">\n<li>\u9876\u70b9\u7684\u5750\u6807<\/li>\n<li>\u7126\u70b9\u7684\u5750\u6807<\/li>\n<li>\u51c6\u7ebf\u7684\u65b9\u7a0b<\/li>\n<li>\u5bf9\u79f0\u8f74\u7684\u65b9\u7a0b<\/li>\n<li>\u4e0ex\u8f74\u7684\u4ea4\u70b9\uff08\u5982\u679c\u6709\uff09<\/li>\n<li>\u6700\u540e\uff0c\u4f7f\u7528\u6536\u96c6\u5230\u7684\u4fe1\u606f\u6784\u5efa\u56fe\u5f62\u8349\u56fe\u3002<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-xAUdvfTRbjw\/YIbmIXDdT-I\/AAAAAAAAFAI\/8NH0t_EWbH0KIuFDnsRu2IyHdyN4WU54wCLcBGAsYHQ\/s0\/caracterizaci%25C3%25B3n%2Bde%2Bpar%25C3%25A1bolas.PNG\" alt=\"\u629b\u7269\u7ebf\u7684\u8868\u5f81\" class=\" aligncenter lazyload\" width=\"537\" height=\"414\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-xAUdvfTRbjw\/YIbmIXDdT-I\/AAAAAAAAFAI\/8NH0t_EWbH0KIuFDnsRu2IyHdyN4WU54wCLcBGAsYHQ\/s0\/caracterizaci%25C3%25B3n%2Bde%2Bpar%25C3%25A1bolas.PNG\" alt=\"\u629b\u7269\u7ebf\u7684\u8868\u5f81\" class=\" aligncenter lazyload\" width=\"537\" height=\"414\" \/><\/noscript><br \/>\n<a name=\"2\"><\/a><\/p>\n<h2>\u4ece\u4e00\u822c\u65b9\u7a0b\u8868\u5f81\u629b\u7269\u7ebf<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=316s\" target=\"_blank\" rel=\"noopener\"><strong>\u5982\u679c\u4f60\u901a\u8fc7<\/strong><\/a> \u4e00\u822c\u65b9\u7a0b\u63cf\u8ff0\u629b\u7269\u7ebf\uff0c\u90a3\u4e48\u4f60\u51e0\u4e4e\u5df2\u7ecf\u638c\u63e1\u4e86\u5b8c\u6210\u8868\u5f81\u6240\u9700\u7684\u5927\u90e8\u5206\u4fe1\u606f\uff0c\u53ea\u6709\u4e0ex\u8f74\u7684\u4ea4\u70b9\u9700\u8981\u8fdb\u4e00\u6b65\u5206\u6790\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x-x_0)^2 =4f(y-y_0)<\/span>\n<p style=\"text-align: justify;\">\u7531\u6b64\u4f60\u5df2\u7ecf\u5f97\u51fa\uff1a<\/p>\n<ul style=\"text-align: justify;\">\n<li><strong>\u9876\u70b9\uff1a<\/strong>\u5750\u6807\u70b9<span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0)<\/span><\/li>\n<li><strong>\u7126\u70b9\u4f4d\u7f6e\uff1a<\/strong>\u8ddd\u9876\u70b9<span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>\u4e2a\u5355\u4f4d<\/li>\n<li><strong>\u7126\u70b9\uff1a<\/strong>\u5750\u6807\u70b9<span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0 + f)<\/span><\/li>\n<li><strong>\u51c6\u7ebf\uff1a<\/strong>\u65b9\u7a0b\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">y= y_0 - f<\/span>\u7684\u76f4\u7ebf<\/li>\n<li><strong>\u5bf9\u79f0\u8f74\uff1a<\/strong>\u65b9\u7a0b\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">x= x_0<\/span>\u7684\u76f4\u7ebf<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u8981\u627e\u5230\u4e0ex\u8f74\u7684\u4ea4\u70b9\uff0c\u4f60\u9700\u8981\u5c06\u4e00\u822c\u65b9\u7a0b\u8f6c\u6362\u4e3a\u6807\u51c6\u5f62\u5f0f\uff0c\u5e76\u5c06\u6240\u5f97\u7684\u4e8c\u6b21\u591a\u9879\u5f0f\u7b49\u4e8e\u96f6\u3002\u5982\u679c\u6709\u89e3\uff0c\u8fd9\u4e9b\u89e3\u5c31\u662f\u4e0ex\u8f74\u7684\u4ea4\u70b9\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u4ece\u6807\u51c6\u65b9\u7a0b\u8868\u5f81\u629b\u7269\u7ebf<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=393s\" target=\"_blank\" rel=\"noopener\"><strong>\u5f53\u629b\u7269\u7ebf\u7684\u65b9\u7a0b<\/strong><\/a>\u4ee5\u6807\u51c6\u5f62\u5f0f\u5448\u73b0\u65f6\uff0c\u4f60\u6709\u4e24\u79cd\u9009\u62e9\uff1a1) \u5c06\u5176\u8f6c\u6362\u4e3a\u4e00\u822c\u65b9\u7a0b\u8fdb\u884c\u8868\u5f81\uff0c\u6216\u8005 2) \u4f7f\u7528\u5bf9\u79f0\u6027\u548c\u4e0ex\u8f74\u7684\u4ea4\u70b9\u3002\u4e24\u79cd\u65b9\u6cd5\u5404\u6709\u4f18\u70b9\u3002\u7b2c\u4e8c\u79cd\u901a\u5e38\u8f83\u5feb\uff0c\u4f46\u629b\u7269\u7ebf\u5e76\u4e0d\u603b\u662f\u4e0ex\u8f74\u76f8\u4ea4\uff0c\u7b2c\u4e00\u79cd\u867d\u7136\u8f83\u4e3a\u7e41\u7410\uff0c\u4f46\u6b63\u5982\u6211\u4eec\u7a0d\u540e\u5c06\u770b\u5230\u7684\uff0c\u5b83\u4e5f\u6613\u4e8e\u81ea\u52a8\u5316\u3002\u6211\u4eec\u5c06\u63a2\u8ba8\u4e24\u79cd\u9009\u62e9\uff0c\u4ee5\u4fbf\u4f60\u6839\u636e\u81ea\u5df1\u7684\u504f\u597d\u548c\u9700\u6c42\u9009\u62e9\u5408\u9002\u7684\u9014\u5f84\u3002<\/p>\n<h3>\u8f6c\u6362\u4e3a\u4e00\u822c\u65b9\u7a0b<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=475s\" target=\"_blank\" rel=\"noopener\"><strong>\u8f6c\u6362\u4e3a\u4e00\u822c\u5f62\u5f0f<\/strong><\/a>\u662f\u901a\u8fc7\u4ee5\u4e0b\u63a8\u7406\u5b8c\u6210\u7684\uff0c\u5176\u4e2d<span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{R}<\/span>\u5e76\u4e14<span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0.<\/span>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td width=\"50\">(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=ax^2 + bx + c<\/span><\/td>\n<td>; \u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=a\\left[x^2 + \\dfrac{b}{a}x + \\dfrac{c}{a}\\right]<\/span><\/td>\n<td>; \u56e0\u5f0f\u5206\u89e3<span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=a\\left[ \\left(x + \\dfrac{b}{2a}\\right)^2 - \\dfrac{b^2}{4a^2} + \\dfrac{c}{a}\\right]<\/span><\/td>\n<td>; \u56e0\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">\\left(x + \\dfrac{b}{2a}\\right)^2 = x^2 + \\dfrac{b}{a}x + \\dfrac{b^2}{4a^2}<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=a\\left[ \\left(x + \\dfrac{b}{2a}\\right)^2 + \\dfrac{4ac - b^2}{4a^2} \\right]<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=a \\left(x + \\dfrac{b}{2a}\\right)^2 + \\dfrac{4ac - b^2}{4a}<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=a \\left(x + \\dfrac{b}{2a}\\right)^2 + \\left(c - \\dfrac{b^2}{4a}\\right)<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\left[x - \\left(- \\dfrac{b}{2a}\\right)\\right]^2 = \\dfrac{1}{a} \\left[y - \\left(c - \\dfrac{b^2}{4a}\\right)\\right]<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\left[x - \\left( -\\dfrac{b}{2a}\\right)\\right]^2 = 4\\left(\\dfrac{1}{4a}\\right) \\left[y - \\left(c - \\dfrac{b^2}{4a}\\right)\\right]<\/span><\/td>\n<td>; \u629b\u7269\u7ebf\u7684\u4e00\u822c\u65b9\u7a0b<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u4ece\u4e2d\u6211\u4eec\u53ef\u4ee5\u63d0\u53d6\u51fa\u4e0e\u6807\u51c6\u65b9\u7a0b\u76f8\u5bf9\u5e94\u7684\u4fe1\u606f\uff0c\u5f97\u51fa\u4ee5\u4e0b\u7ed3\u8bba\uff1a<\/p>\n<ul style=\"text-align: justify;\">\n<li><strong>\u9876\u70b9\uff1a<\/strong>\u5750\u6807\u70b9<span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0) = \\left(-\\dfrac{b}{2a}, c -\\dfrac{b^2}{4a} \\right)<\/span><\/li>\n<li><strong>\u7126\u70b9\u4f4d\u7f6e\uff1a<\/strong>\u8ddd\u9876\u70b9<span class=\"katex-eq\" data-katex-display=\"false\">f = \\dfrac{1}{4a}<\/span>\u4e2a\u5355\u4f4d<\/li>\n<li><strong>\u7126\u70b9\uff1a<\/strong>\u5750\u6807\u70b9<span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0 + f) = \\left(-\\dfrac{b}{2a}, c -\\dfrac{b^2}{4a} + \\dfrac{1}{4a}\\right) =\\left(-\\dfrac{b}{2a}, c +\\dfrac{1-b^2}{4a}\\right) <\/span><\/li>\n<li><strong>\u51c6\u7ebf\uff1a<\/strong>\u65b9\u7a0b\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">y=y_0 - f= c -\\dfrac{b^2}{4a} - \\dfrac{1}{4a} = c -\\dfrac{1 + b^2}{4a}<\/span><\/li>\n<li><strong>\u5bf9\u79f0\u8f74\uff1a<\/strong>\u65b9\u7a0b\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">x= x_0 = -\\dfrac{b}{2a}<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u4ece\u8fd9\u91cc\uff0c\u629b\u7269\u7ebf\u7684\u8868\u5f81\u5c31\u50cf\u6211\u4eec\u5df2\u7ecf\u770b\u5230\u7684\u90a3\u6837\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e00\u822c\u65b9\u7a0b\u5b8c\u6210\u3002<\/p>\n<h3>\u4f7f\u7528\u5bf9\u79f0\u6027\u548c\u4e0ex\u8f74\u7684\u4ea4\u70b9<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=769s\" target=\"_blank\" rel=\"noopener\"><strong>\u5f53\u6211\u4eec\u4f7f\u7528<\/strong><\/a>\u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b<span class=\"katex-eq\" data-katex-display=\"false\">y=ax^2 + bx+c<\/span>\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u8ba1\u7b97\u51fa\u5b83\u4e0ex\u8f74\u7684\u4ea4\u70b9\uff0c\u53ea\u9700\u89e3\u65b9\u7a0b\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">ax^2 + bx + c = 0<\/span>\n<p style=\"text-align: justify;\">\u5982\u679c\u89e3\u5b58\u5728\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u4ea4\u70b9<span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">x_2<\/span>\uff0c\u5206\u522b\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1 = \\dfrac{-b + \\sqrt{b^2-4ac}}{2a}<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x_2 = \\dfrac{-b - \\sqrt{b^2-4ac}}{2a}<\/span>\n<p style=\"text-align: justify;\">\u7531\u4e8e\u629b\u7269\u7ebf\u662f\u5bf9\u79f0\u7684\uff0c\u6211\u4eec\u7684\u5bf9\u79f0\u8f74\u65b9\u7a0b\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x = x_0 = \\dfrac{x_1 + x_2}{2}= -\\dfrac{b}{2a}<\/span>\n<p style=\"text-align: justify;\">\u5bf9\u79f0\u8f74\u5fc5\u987b\u901a\u8fc7\u629b\u7269\u7ebf\u7684\u9876\u70b9\uff0c\u5176\u5750\u6807\u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_0, y_0) = (x_0, y(x_0)) = \\left( -\\dfrac{b}{2a}, y\\left(-\\dfrac{b}{2a}\\right) \\right)<\/span>\n<p style=\"text-align: justify;\">\u5176\u4e2d\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y_0 = y\\left(-\\dfrac{b}{2a} \\right) = a\\left(-\\dfrac{b}{2a}\\right)^2 + b\\left(-\\dfrac{b}{2a}\\right) + c = \\dfrac{b^2}{4a} - \\dfrac{b^2}{2a} + c = c - \\dfrac{b^2}{4a}<\/span>\n<p style=\"text-align: justify;\">\u8fd9\u5c31\u662f\u6211\u4eec\u901a\u8fc7\u5176\u4ed6\u65b9\u6cd5\u5f97\u51fa\u7684\u9876\u70b9\u5750\u6807\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_0, y_0) = \\left( -\\dfrac{b}{2a},c - \\dfrac{b^2}{4a} \\right)<\/span>\n<p style=\"text-align: justify;\">\u7126\u70b9\u7684\u4f4d\u7f6e\u4e0e\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\u4e00\u6837\uff0c\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">f=\\dfrac{1}{4a},<\/span>\u4ece\u800c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa\u51c6\u7ebf\u3001\u7126\u70b9\u4ee5\u53ca\u4ece\u4e00\u822c\u65b9\u7a0b\u4e2d\u5f97\u5230\u7684\u6240\u6709\u4fe1\u606f\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u4f7f\u7528Excel\u8fdb\u884c\u81ea\u52a8\u8868\u5f81<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=1086s\" target=\"_blank\" rel=\"noopener\"><strong>\u5b8c\u6210\u4e86\u6240\u6709\u63a8\u7406\u4e4b\u540e<\/strong><\/a>\uff0c\u73b0\u5728\u901a\u8fc7Excel\u81ea\u52a8\u5316\u4efb\u4f55\u629b\u7269\u7ebf\u7684\u8868\u5f81\u53d8\u5f97\u975e\u5e38\u7b80\u5355\u3002\u4f60\u53ef\u4ee5\u5728\u6b64\u5904\u627e\u5230\u4e00\u4e2a\u793a\u4f8b <a href=\"https:\/\/drive.google.com\/file\/d\/1LbNOKHHfzlPgHI3_NSzuB_6_b7KmXlTd\/view?usp=sharing\" rel=\"noopener\" target=\"_blank\">\u8fd9\u91cc\u3002<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u629b\u7269\u7ebf\u53ca\u5176\u56fe\u5f62\u7684\u8868\u5f81 \u6458\u8981: \u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u4ece\u4e00\u822c\u65b9\u7a0b\u548c\u6807\u51c6\u5f62\u5f0f\u51fa\u53d1\uff0c\u89e3\u91ca\u5982\u4f55\u8bc6\u522b\u5173\u952e\u5143\u7d20\uff0c\u5982\u9876\u70b9\u3001\u7126\u70b9\u3001\u51c6\u7ebf\u3001\u5bf9\u79f0\u8f74\u4ee5\u53ca\u53ef\u80fd\u7684\u4e0eX\u8f74\u7684\u4ea4\u70b9\u3002 \u5b66\u4e60\u76ee\u6807: \u672c\u8282\u8bfe\u7ed3\u675f\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u8ba1\u7b97\u9876\u70b9\u3001\u7126\u70b9\u548c\u51c6\u7ebf\u7684\u4f4d\u7f6e\uff0c\u4ece\u5176\u4e00\u822c\u5f62\u5f0f\u548c\u6807\u51c6\u5f62\u5f0f\u51fa\u53d1\u3002 \u8f6c\u6362\u6807\u51c6\u65b9\u7a0b\u4e3a\u4e00\u822c\u5f62\u5f0f\u4ee5\u63d0\u53d6\u51e0\u4f55\u4fe1\u606f\u3002 \u7ed8\u5236\u4f7f\u7528\u83b7\u5f97\u7684\u4fe1\u606f\u7ed8\u5236\u629b\u7269\u7ebf\u7684\u56fe\u5f62\u3002 \u5185\u5bb9\u7d22\u5f15 \u629b\u7269\u7ebf\u7684\u4e00\u822c\u5f62\u5f0f\u548c\u6807\u51c6\u5f62\u5f0f \u4ece\u4e00\u822c\u65b9\u7a0b\u8868\u5f81\u629b\u7269\u7ebf \u4ece\u6807\u51c6\u65b9\u7a0b\u8868\u5f81\u629b\u7269\u7ebf \u4f7f\u7528Excel\u8fdb\u884c\u81ea\u52a8\u8868\u5f81 \u629b\u7269\u7ebf\u7684\u4e00\u822c\u5f62\u5f0f\u548c\u6807\u51c6\u5f62\u5f0f \u5728\u4e0a\u4e00\u8bfe\u4e2d\uff0c\u6211\u4eec\u770b\u5230\u629b\u7269\u7ebf\u53ef\u4ee5\u901a\u8fc7\u629b\u7269\u7ebf\u7684\u4e00\u822c\u65b9\u7a0b\u4ee3\u6570\u5730\u8868\u793a\u3002 \u5176\u4e2d\u5750\u6807\u5bf9\u662f\u9876\u70b9\u7684\u4f4d\u7f6e\uff0c\u662f\u7126\u8ddd\u3002\u5982\u679c\uff0c\u90a3\u4e48\u7126\u70b9\u5728\u9876\u70b9\u4e4b\u4e0a\u7684\u8ddd\u79bb\uff1b\u5982\u679c\uff0c\u5219\u7126\u70b9\u5728\u9876\u70b9\u4e4b\u4e0b\u7684\u8ddd\u79bb\u3002 \u6211\u4eec\u8fd8\u770b\u5230\uff0c\u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\u5f62\u5f0f\u7b49\u6548\u4e8e\u4e8c\u6b21\u591a\u9879\u5f0f\u3002 \u5176\u4e2d \u8868\u5f81\u629b\u7269\u7ebf\u5c31\u662f\u63ed\u793a\u4ee5\u4e0b\u4fe1\u606f\u3002 \u9876\u70b9\u7684\u5750\u6807 \u7126\u70b9\u7684\u5750\u6807 \u51c6\u7ebf\u7684\u65b9\u7a0b \u5bf9\u79f0\u8f74\u7684\u65b9\u7a0b \u4e0ex\u8f74\u7684\u4ea4\u70b9\uff08\u5982\u679c\u6709\uff09 \u6700\u540e\uff0c\u4f7f\u7528\u6536\u96c6\u5230\u7684\u4fe1\u606f\u6784\u5efa\u56fe\u5f62\u8349\u56fe\u3002 \u4ece\u4e00\u822c\u65b9\u7a0b\u8868\u5f81\u629b\u7269\u7ebf \u5982\u679c\u4f60\u901a\u8fc7 \u4e00\u822c\u65b9\u7a0b\u63cf\u8ff0\u629b\u7269\u7ebf\uff0c\u90a3\u4e48\u4f60\u51e0\u4e4e\u5df2\u7ecf\u638c\u63e1\u4e86\u5b8c\u6210\u8868\u5f81\u6240\u9700\u7684\u5927\u90e8\u5206\u4fe1\u606f\uff0c\u53ea\u6709\u4e0ex\u8f74\u7684\u4ea4\u70b9\u9700\u8981\u8fdb\u4e00\u6b65\u5206\u6790\u3002 \u7531\u6b64\u4f60\u5df2\u7ecf\u5f97\u51fa\uff1a \u9876\u70b9\uff1a\u5750\u6807\u70b9 \u7126\u70b9\u4f4d\u7f6e\uff1a\u8ddd\u9876\u70b9\u4e2a\u5355\u4f4d \u7126\u70b9\uff1a\u5750\u6807\u70b9 \u51c6\u7ebf\uff1a\u65b9\u7a0b\u4e3a\u7684\u76f4\u7ebf \u5bf9\u79f0\u8f74\uff1a\u65b9\u7a0b\u4e3a\u7684\u76f4\u7ebf \u8981\u627e\u5230\u4e0ex\u8f74\u7684\u4ea4\u70b9\uff0c\u4f60\u9700\u8981\u5c06\u4e00\u822c\u65b9\u7a0b\u8f6c\u6362\u4e3a\u6807\u51c6\u5f62\u5f0f\uff0c\u5e76\u5c06\u6240\u5f97\u7684\u4e8c\u6b21\u591a\u9879\u5f0f\u7b49\u4e8e\u96f6\u3002\u5982\u679c\u6709\u89e3\uff0c\u8fd9\u4e9b\u89e3\u5c31\u662f\u4e0ex\u8f74\u7684\u4ea4\u70b9\u3002 \u4ece\u6807\u51c6\u65b9\u7a0b\u8868\u5f81\u629b\u7269\u7ebf \u5f53\u629b\u7269\u7ebf\u7684\u65b9\u7a0b\u4ee5\u6807\u51c6\u5f62\u5f0f\u5448\u73b0\u65f6\uff0c\u4f60\u6709\u4e24\u79cd\u9009\u62e9\uff1a1) \u5c06\u5176\u8f6c\u6362\u4e3a\u4e00\u822c\u65b9\u7a0b\u8fdb\u884c\u8868\u5f81\uff0c\u6216\u8005 2) \u4f7f\u7528\u5bf9\u79f0\u6027\u548c\u4e0ex\u8f74\u7684\u4ea4\u70b9\u3002\u4e24\u79cd\u65b9\u6cd5\u5404\u6709\u4f18\u70b9\u3002\u7b2c\u4e8c\u79cd\u901a\u5e38\u8f83\u5feb\uff0c\u4f46\u629b\u7269\u7ebf\u5e76\u4e0d\u603b\u662f\u4e0ex\u8f74\u76f8\u4ea4\uff0c\u7b2c\u4e00\u79cd\u867d\u7136\u8f83\u4e3a\u7e41\u7410\uff0c\u4f46\u6b63\u5982\u6211\u4eec\u7a0d\u540e\u5c06\u770b\u5230\u7684\uff0c\u5b83\u4e5f\u6613\u4e8e\u81ea\u52a8\u5316\u3002\u6211\u4eec\u5c06\u63a2\u8ba8\u4e24\u79cd\u9009\u62e9\uff0c\u4ee5\u4fbf\u4f60\u6839\u636e\u81ea\u5df1\u7684\u504f\u597d\u548c\u9700\u6c42\u9009\u62e9\u5408\u9002\u7684\u9014\u5f84\u3002 \u8f6c\u6362\u4e3a\u4e00\u822c\u65b9\u7a0b \u8f6c\u6362\u4e3a\u4e00\u822c\u5f62\u5f0f\u662f\u901a\u8fc7\u4ee5\u4e0b\u63a8\u7406\u5b8c\u6210\u7684\uff0c\u5176\u4e2d\u5e76\u4e14 (1) ; \u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b ; \u56e0\u5f0f\u5206\u89e3 ; \u56e0\u4e3a ; \u629b\u7269\u7ebf\u7684\u4e00\u822c\u65b9\u7a0b \u4ece\u4e2d\u6211\u4eec\u53ef\u4ee5\u63d0\u53d6\u51fa\u4e0e\u6807\u51c6\u65b9\u7a0b\u76f8\u5bf9\u5e94\u7684\u4fe1\u606f\uff0c\u5f97\u51fa\u4ee5\u4e0b\u7ed3\u8bba\uff1a \u9876\u70b9\uff1a\u5750\u6807\u70b9 \u7126\u70b9\u4f4d\u7f6e\uff1a\u8ddd\u9876\u70b9\u4e2a\u5355\u4f4d \u7126\u70b9\uff1a\u5750\u6807\u70b9 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28929,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":7,"footnotes":""},"categories":[591,575],"tags":[],"class_list":["post-28935","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-591","category-575"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u629b\u7269\u7ebf\u53ca\u5176\u56fe\u5f62\u7684\u8868\u5f81 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u5b66\u4e60\u901a\u8fc7\u8bc6\u522b\u9876\u70b9\u3001\u7126\u70b9\u3001\u51c6\u7ebf\u3001\u5bf9\u79f0\u8f74\u548c\u4e0ex\u8f74\u7684\u4ea4\u70b9\u6765\u8868\u5f81\u629b\u7269\u7ebf\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/zh\/\u629b\u7269\u7ebf\u53ca\u5176\u56fe\u5f62\u7684\u8868\u5f81\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u629b\u7269\u7ebf\u53ca\u5176\u56fe\u5f62\u7684\u8868\u5f81\" \/>\n<meta property=\"og:description\" content=\"\u5b66\u4e60\u901a\u8fc7\u8bc6\u522b\u9876\u70b9\u3001\u7126\u70b9\u3001\u51c6\u7ebf\u3001\u5bf9\u79f0\u8f74\u548c\u4e0ex\u8f74\u7684\u4ea4\u70b9\u6765\u8868\u5f81\u629b\u7269\u7ebf\u3002\" \/>\n<meta property=\"og:url\" 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