{"id":28905,"date":"2021-04-23T13:00:39","date_gmt":"2021-04-23T13:00:39","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28905"},"modified":"2024-09-22T02:11:16","modified_gmt":"2024-09-22T02:11:16","slug":"%e6%8a%9b%e7%89%a9%e7%ba%bf%e6%96%b9%e7%a8%8b%ef%bc%9a%e5%ae%9a%e4%b9%89%e5%92%8c%e6%80%a7%e8%b4%a8","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e6%8a%9b%e7%89%a9%e7%ba%bf%e6%96%b9%e7%a8%8b%ef%bc%9a%e5%ae%9a%e4%b9%89%e5%92%8c%e6%80%a7%e8%b4%a8\/","title":{"rendered":"\u629b\u7269\u7ebf\u65b9\u7a0b\uff1a\u5b9a\u4e49\u548c\u6027\u8d28"},"content":{"rendered":"<p><center><\/p>\n<h1>\u629b\u7269\u7ebf\u65b9\u7a0b\uff1a\u5b9a\u4e49\u548c\u6027\u8d28<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n   \u672c\u8bfe\u7a0b\u63a2\u8ba8\u4e86\u629b\u7269\u7ebf\u65b9\u7a0b\u7684\u5b9a\u4e49\u548c\u63a8\u5bfc\uff0c\u7a81\u51fa\u5176\u4f5c\u4e3a\u5230\u7126\u70b9\u548c\u51c6\u7ebf\u7b49\u8ddd\u79bb\u7684\u70b9\u96c6\u5408\u7684\u8d77\u6e90\u3002\u5728\u6b64\u6982\u5ff5\u7684\u57fa\u7840\u4e0a\uff0c\u56de\u987e\u4e86\u8bf8\u5982\u7b1b\u5361\u5c14\u5e73\u9762\u4e2d\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u548c\u56fe\u5f62\u5e73\u79fb\u7b49\u5148\u524d\u7684\u6982\u5ff5\uff0c\u4ece\u800c\u5f15\u5165\u4e86\u629b\u7269\u7ebf\u7684\u57fa\u672c\u65b9\u7a0b\u53ca\u5176\u4e0e\u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u5173\u7cfb\u3002\u6700\u540e\uff0c\u63a8\u5bfc\u51fa\u4e86\u4efb\u610f\u9876\u70b9\u7684\u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b\uff0c\u5e76\u5c06\u5176\u8f6c\u5316\u4e3a\u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u6807\u51c6\u5f62\u5f0f\u3002<br \/>\n   <\/em><\/p>\n<p><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n   \u5b8c\u6210\u672c\u8bfe\u7a0b\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u7406\u89e3<\/strong>\u629b\u7269\u7ebf\u7684\u51e0\u4f55\u5b9a\u4e49\uff0c\u4f5c\u4e3a\u5230\u7126\u70b9\u548c\u51c6\u7ebf\u7b49\u8ddd\u79bb\u7684\u70b9\u96c6\u5408\u3002<\/li>\n<li><strong>\u63a8\u5bfc<\/strong>\u629b\u7269\u7ebf\u7684\u57fa\u672c\u65b9\u7a0b\uff0c\u5229\u7528\u7126\u70b9-\u51c6\u7ebf\u7684\u8ddd\u79bb\u5173\u7cfb\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u629b\u7269\u7ebf\u4e0e\u4e8c\u6b21\u591a\u9879\u5f0f\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u63a8\u5bfc<\/strong>\u4efb\u610f\u9876\u70b9(h,k)\u7684\u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b\u3002<\/li>\n<\/ol>\n<p>   <strong>\u5185\u5bb9\u7d22\u5f15<\/strong><br \/>\n   <a href=\"#1\"><strong>\u629b\u7269\u7ebf\u65b9\u7a0b\u63a8\u5bfc\u7684\u5148\u524d\u6982\u5ff5<\/strong><\/a><br \/>\n   <a href=\"#2\">\u629b\u7269\u7ebf\u7684\u51e0\u4f55\u6982\u5ff5<\/a><br \/>\n   <a href=\"#3\">\u7b1b\u5361\u5c14\u5e73\u9762\u4e2d\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb<\/a><br \/>\n   <a href=\"#4\">\u56fe\u5f62\u7684\u5e73\u79fb<\/a><br \/>\n   <a href=\"#5\"><strong>\u629b\u7269\u7ebf\u7684\u5b9a\u4e49<\/strong><\/a><br \/>\n   <a href=\"#6\">\u629b\u7269\u7ebf\u57fa\u672c\u65b9\u7a0b\u7684\u63a8\u5bfc<\/a><br \/>\n   <a href=\"#7\">\u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b<\/a><br \/>\n   <a href=\"#8\">\u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\u4e0e\u4e8c\u6b21\u591a\u9879\u5f0f<\/a>\n   <\/p>\n<p><\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/O2EYxxK03jU\" title=\"YouTube\u89c6\u9891\u64ad\u653e\u5668\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u629b\u7269\u7ebf\u65b9\u7a0b\u63a8\u5bfc\u7684\u5148\u524d\u6982\u5ff5<\/h2>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u629b\u7269\u7ebf\u7684\u51e0\u4f55\u6982\u5ff5<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=130s\" target=\"_blank\" rel=\"noopener\"><strong>\u629b\u7269\u7ebf\u662f\u4e00\u6761\u66f2\u7ebf<\/strong><\/a>\uff0c\u5b83\u662f\u6240\u6709\u5230\u56fa\u5b9a\u70b9\uff08\u79f0\u4e3a\u7126\u70b9\uff09\u548c\u56fa\u5b9a\u76f4\u7ebf\uff08\u79f0\u4e3a\u51c6\u7ebf\uff09\u7684\u70b9\u7684\u96c6\u5408\u3002\u4e3a\u4e86\u7406\u89e3\u8fd9\u4e00\u5b9a\u4e49\uff0c\u5e76\u5c06\u5176\u8f6c\u5316\u4e3a\u6211\u4eec\u53ef\u4ee5\u64cd\u4f5c\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u2014\u2014\u629b\u7269\u7ebf\u65b9\u7a0b\uff0c\u9996\u5148\u9700\u8981\u56de\u987e\u4e00\u4e9b\u5148\u524d\u7684\u6982\u5ff5\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u7b1b\u5361\u5c14\u5e73\u9762\u4e2d\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=199s\" target=\"_blank\" rel=\"noopener\"><strong>\u8003\u8651\u4e24\u4e2a\u70b9<\/strong><\/a><span class=\"katex-eq\" data-katex-display=\"false\">p_1 = (x_1, y_1)<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">p_2 = (x_2, y_2)<\/span>\u3002\u5b83\u4eec\u4e4b\u95f4\u7684\u8ddd\u79bb\u662f\u8fde\u63a5\u5b83\u4eec\u7684\u7ebf\u6bb5\u7684\u957f\u5ea6\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-Nm00_Mr0PJE\/YIH_4rGiO0I\/AAAAAAAAE-s\/gLJ6gjIGUuwsDhwVt6pa3MDZ0YQXEgJVgCLcBGAsYHQ\/s0\/distancia.PNG\" alt=\"\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\" class=\"aligncenter lazyload\" width=\"409\" height=\"263\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-Nm00_Mr0PJE\/YIH_4rGiO0I\/AAAAAAAAE-s\/gLJ6gjIGUuwsDhwVt6pa3MDZ0YQXEgJVgCLcBGAsYHQ\/s0\/distancia.PNG\" alt=\"\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\" class=\"aligncenter lazyload\" width=\"409\" height=\"263\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7<a href=\"https:\/\/youtu.be\/grjSzVl8Acw?t=553\" target=\"_blank\" rel=\"noopener\">\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b9a\u7406<\/a> \u6765\u8ba1\u7b97\u8fd9\u4e00\u8ddd\u79bb\uff0c\u56fe\u5f62\u5982\u4e0b\uff1a<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-xOGFNRBeUU0\/YIIAohgMqNI\/AAAAAAAAE-0\/LCiSnSMHVwMpTGOnTchVFtkVL0izESn3ACLcBGAsYHQ\/s0\/teorema%2Bde%2Bpitagoras.PNG\" alt=\"\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b9a\u7406\" class=\" aligncenter lazyload\" width=\"404\" height=\"255\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-xOGFNRBeUU0\/YIIAohgMqNI\/AAAAAAAAE-0\/LCiSnSMHVwMpTGOnTchVFtkVL0izESn3ACLcBGAsYHQ\/s0\/teorema%2Bde%2Bpitagoras.PNG\" alt=\"\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b9a\u7406\" class=\" aligncenter lazyload\" width=\"404\" height=\"255\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u56e0\u6b64\uff0c\u4e24\u4e2a\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u4e3a\uff1a<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">d= \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u56fe\u5f62\u7684\u5e73\u79fb<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=390s\" target=\"_blank\" rel=\"noopener\"><strong>\u8003\u8651\u51fd\u6570<\/strong><\/a><span class=\"katex-eq\" data-katex-display=\"false\">y(x) = x^2<\/span>\u3002\u7ed8\u5236\u56fe\u5f62\u540e\uff0c\u5c06\u5f97\u5230\u5982\u4e0b\u56fe\u6240\u793a\u7684\u7ed3\u679c\uff1a<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-hf1AvDmNoYc\/YIIhv8_zkjI\/AAAAAAAAE_E\/kedKQoFwJSIkoIZgev9cQS--frmDbwTOwCLcBGAsYHQ\/s0\/traslacionDeGraficos1.PNG\" alt=\"\u56fe\u5f62\u5e73\u79fb\" class=\" aligncenter lazyload\" width=\"325\" height=\"321\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-hf1AvDmNoYc\/YIIhv8_zkjI\/AAAAAAAAE_E\/kedKQoFwJSIkoIZgev9cQS--frmDbwTOwCLcBGAsYHQ\/s0\/traslacionDeGraficos1.PNG\" alt=\"\u56fe\u5f62\u5e73\u79fb\" class=\" aligncenter lazyload\" width=\"325\" height=\"321\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u5982\u679c\u5728\u8be5\u51fd\u6570\u4e2d\u5c06 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u66ff\u6362\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">x-1<\/span>\uff0c\u5e76\u5c06 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u66ff\u6362\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">y-1<\/span>\uff0c\u6211\u4eec\u5c06\u770b\u5230\u56fe\u5f62\u7684\u4ee5\u4e0b\u53d8\u5316\uff1a<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-TRHquCBRoB4\/YIIjbaFx5WI\/AAAAAAAAE_M\/ngYFLBH4y6AS4ywUaSwo2sscmAVT6viHgCLcBGAsYHQ\/s0\/traslacionDeGraficos2.PNG\" alt=\"\u56fe\u5f62\u5e73\u79fb\" class=\" aligncenter lazyload\" width=\"352\" height=\"288\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-TRHquCBRoB4\/YIIjbaFx5WI\/AAAAAAAAE_M\/ngYFLBH4y6AS4ywUaSwo2sscmAVT6viHgCLcBGAsYHQ\/s0\/traslacionDeGraficos2.PNG\" alt=\"\u56fe\u5f62\u5e73\u79fb\" class=\" aligncenter lazyload\" width=\"352\" height=\"288\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u901a\u5e38\uff0c\u6bcf\u6b21\u6b64\u7c7b\u66ff\u6362\u90fd\u4f1a\u4ea7\u751f\u5e73\u79fb\u53d8\u6362\uff0c\u5177\u4f53\u5982\u4e0b\uff1a<\/p>\n<ul style=\"text-align: justify;\">\n<li><strong><span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto x-a<\/span>\uff1a<\/strong>\u82e5 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u4e3a\u6b63\uff0c\u5219\u5411\u53f3\u79fb\u52a8 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u4e2a\u5355\u4f4d\uff1b\u82e5\u4e3a\u8d1f\uff0c\u5219\u5411\u5de6\u79fb\u52a8\u3002<\/li>\n<li><strong><span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto y-b<\/span>\uff1a<\/strong>\u82e5 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u4e3a\u6b63\uff0c\u5219\u5411\u4e0a\u79fb\u52a8 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u4e2a\u5355\u4f4d\uff1b\u82e5\u4e3a\u8d1f\uff0c\u5219\u5411\u4e0b\u79fb\u52a8\u3002<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u8fd9\u4e9b\u662f\u5e73\u79fb\u53d8\u6362\uff0c\u5b83\u4eec\u7684\u6548\u679c\u603b\u7ed3\u5728\u4e0b\u56fe\u4e2d\uff1a<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-anQa6JMVTyA\/YIIm1AgBVbI\/AAAAAAAAE_U\/7aKD9WSMVawEwJXOnpqpr-cskL-NxoPUgCLcBGAsYHQ\/s0\/traslacionDeGraficos3.PNG\" alt=\"\u56fe\u5f62\u7684\u901a\u7528\u5e73\u79fb\" class=\"aligncenter lazyload\" width=\"522\" height=\"314\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-anQa6JMVTyA\/YIIm1AgBVbI\/AAAAAAAAE_U\/7aKD9WSMVawEwJXOnpqpr-cskL-NxoPUgCLcBGAsYHQ\/s0\/traslacionDeGraficos3.PNG\" alt=\"\u56fe\u5f62\u7684\u901a\u7528\u5e73\u79fb\" class=\"aligncenter lazyload\" width=\"522\" height=\"314\" \/><\/noscript><br \/>\n<a name=\"5\"><\/a><\/p>\n<h2>\u629b\u7269\u7ebf\u7684\u5b9a\u4e49<\/h2>\n<p style=\"text-align: justify;\">\u629b\u7269\u7ebf\u662f\u6240\u6709\u5230\u56fa\u5b9a\u70b9\u548c\u56fa\u5b9a\u76f4\u7ebf\u7b49\u8ddd\u79bb\u7684\u70b9\u7684\u96c6\u5408\u3002<br \/>\n<img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-16fe-qg141I\/YIH4NpKtc4I\/AAAAAAAAE-k\/ILLGwpB_IQQZbUBJvXOIl5HChpo8Noi_gCLcBGAsYHQ\/s0\/Parabola.PNG\" alt=\"\u629b\u7269\u7ebf\u7684\u5b9a\u4e49\" class=\"aligncenter lazyload\" width=\"426\" height=\"302\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-16fe-qg141I\/YIH4NpKtc4I\/AAAAAAAAE-k\/ILLGwpB_IQQZbUBJvXOIl5HChpo8Noi_gCLcBGAsYHQ\/s0\/Parabola.PNG\" alt=\"\u629b\u7269\u7ebf\u7684\u5b9a\u4e49\" class=\"aligncenter lazyload\" width=\"426\" height=\"302\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u56fa\u5b9a\u70b9\u79f0\u4e3a<strong>\u7126\u70b9<\/strong>\uff0c\u56fa\u5b9a\u76f4\u7ebf\u79f0\u4e3a<strong>\u51c6\u7ebf<\/strong>\u3002\u6ce8\u610f\u5230\uff0c\u8ddd\u79bb\u7684\u6982\u5ff5\u5728\u5b9a\u4e49\u629b\u7269\u7ebf\u65f6\u81f3\u5173\u91cd\u8981\uff0c\u56e0\u6b64\u8981\u6df1\u5165\u5206\u6790\uff0c\u6211\u4eec\u5fc5\u987b\u590d\u4e60\u5982\u4f55\u5728\u7b1b\u5361\u5c14\u5e73\u9762\u4e0a\u6d4b\u91cf\u8ddd\u79bb\uff0c\u5e76\u4ee3\u6570\u5316\u8868\u8fbe\u3002<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u629b\u7269\u7ebf\u57fa\u672c\u65b9\u7a0b\u7684\u63a8\u5bfc<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=604s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e3a\u4e86\u7b80\u5316\uff0c\u8003\u8651\u7126\u70b9<\/strong><\/a><span class=\"katex-eq\" data-katex-display=\"false\">p_f= (0,f)<\/span> \u548c\u51c6\u7ebf\u65b9\u7a0b\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">y=-p<\/span>\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-XfDceUwcaFM\/YIIZEUT6DrI\/AAAAAAAAE-8\/keal2s_uSooVvkKsa3Sw1roANTDH8592QCLcBGAsYHQ\/s0\/analisisParabola.PNG\" alt=\"\u629b\u7269\u7ebf\u65b9\u7a0b\" class=\" aligncenter lazyload\" width=\"334\" height=\"249\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-XfDceUwcaFM\/YIIZEUT6DrI\/AAAAAAAAE-8\/keal2s_uSooVvkKsa3Sw1roANTDH8592QCLcBGAsYHQ\/s0\/analisisParabola.PNG\" alt=\"\u629b\u7269\u7ebf\u65b9\u7a0b\" class=\" aligncenter lazyload\" width=\"334\" height=\"249\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u82e5\u53d6\u629b\u7269\u7ebf\u4e0a\u4efb\u610f\u70b9 <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span>\uff0c\u8be5\u70b9\u5230\u7126\u70b9\u548c\u51c6\u7ebf\u7684\u8ddd\u79bb\u76f8\u7b49\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u4ee3\u6570\u65b9\u5f0f\u63cf\u8ff0\uff1a<\/p>\n<p style=\"text-align: center;\">\u7126\u70b9-\u70b9\u8ddd\u79bb <span class=\"katex-eq\" data-katex-display=\"false\">= \\sqrt{x^2 + (f-y)^2}= y+f =<\/span> \u70b9-\u51c6\u7ebf\u8ddd\u79bb<\/p>\n<p style=\"text-align: justify;\">\u4ece\u8fd9\u91cc\u6211\u4eec\u63a8\u5bfc\u51fa\u4ee5\u4e0b\u63a8\u7406\uff1a<\/p>\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\">\\sqrt{x^2 + (f-y)^2}= y+f<\/span><\/td>\n<td>; \u70b9-\u7126\u70b9\u8ddd\u79bb = \u70b9-\u51c6\u7ebf\u8ddd\u79bb\uff0c\u629b\u7269\u7ebf\u5b9a\u4e49<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">x^2 + (f-y)^2= (y+f)^2<\/span><\/td>\n<td>; \u7531 (1)\uff0c\u5e73\u65b9\u4e24\u8fb9<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">x^2 + \\cancel{f^2} - 2fy + \\cancel{y^2}= \\cancel{y^2} + 2fy + \\cancel{f^2}<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">x^2 - 2fy = 2fy <\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{y=\\dfrac{x^2}{4f}}<\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u8fd9\u5c31\u662f\u6211\u4eec\u6240\u8bf4\u7684<strong>\u629b\u7269\u7ebf\u57fa\u672c\u65b9\u7a0b<\/strong>\u3002<\/p>\n<p style=\"text-align: justify;\">\u5982\u679c\u6211\u4eec\u4ed4\u7ec6\u89c2\u5bdf\u8fd9\u6761\u629b\u7269\u7ebf\uff0c\u4f1a\u53d1\u73b0\u6709\u4e00\u4e2a\u70b9\u5177\u6709\u4e0e\u7126\u70b9\u6700\u8fd1\u7684\u6027\u8d28\uff08\u6216\u4e0e\u51c6\u7ebf\u6700\u8fd1\u7684\u6027\u8d28\uff09\u3002\u6b64\u70b9\u79f0\u4e3a<strong>\u9876\u70b9<\/strong>\uff0c\u5728\u6b64\u7279\u5b9a\u60c5\u51b5\u4e0b\u5176\u5750\u6807\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">(0,0)<\/span>\uff1b\u7126\u70b9\u548c\u9876\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u79f0\u4e3a<strong>\u7126\u8ddd<\/strong>\uff0c\u5176\u503c <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u53ef\u4ee5\u662f\u4efb\u610f\u5b9e\u6570\uff0c\u9664\u4e86\u96f6\u3002<\/p>\n<p style=\"text-align: justify;\">\u5f53 <span class=\"katex-eq\" data-katex-display=\"false\">f\\gt 0<\/span> \u65f6\uff0c\u629b\u7269\u7ebf\u5411\u4e0a\u5f00\u53e3\uff1b\u76f8\u53cd\uff0c\u5f53 <span class=\"katex-eq\" data-katex-display=\"false\">f\\lt 0<\/span> \u65f6\uff0c\u629b\u7269\u7ebf\u5411\u4e0b\u5f00\u53e3\u3002\u968f\u7740 <span class=\"katex-eq\" data-katex-display=\"false\">f\\to 0<\/span>\uff0c\u629b\u7269\u7ebf\u4f1a\u9010\u6e10\u53d8\u5e73\uff0c\u4fdd\u6301\u9876\u70b9\u4f4d\u7f6e\u4e0d\u53d8\uff0c\u51c6\u7ebf\u9760\u8fd1\u9876\u70b9\uff0c\u770b\u8d77\u6765\u629b\u7269\u7ebf\u548c\u51c6\u7ebf\u4f1a\u5408\u5e76\u4e3a\u4e00\u6761\u76f4\u7ebf\uff1b\u5f53 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u4e3a\u96f6\u65f6\uff0c\u56fe\u5f62\u6d88\u5931\uff0c\u56e0\u4e3a\u4e0d\u5b58\u5728\u9664\u4ee5\u96f6\u7684\u60c5\u51b5\u3002<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=1007s\" target=\"_blank\" rel=\"noopener\"><strong>\u4ece\u629b\u7269\u7ebf\u7684\u57fa\u672c\u65b9\u7a0b<\/strong><\/a>\u548c\u5e73\u79fb\u56fe\u5f62\u5f97\u51fa\u7684\u7ed3\u679c\u662f\uff0c\u66ff\u6362 <span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto (x-h)<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto (y-k),<\/span> \u540e\u5f97\u51fa<strong>\u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b<\/strong>\uff0c\u9876\u70b9\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">(h,k)<\/span>\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(y-k) = \\dfrac{(x-h)^2}{4f}<\/span>\n<p><a name=\"8\"><\/a><\/p>\n<h3>\u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\u4e0e\u4e8c\u6b21\u591a\u9879\u5f0f<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=1116s\" target=\"_blank\" rel=\"noopener\"><strong>\u5982\u679c\u5c55\u5f00\u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b<\/strong><\/a>\uff0c\u53ef\u4ee5\u63a8\u5bfc\u51fa\u4ee5\u4e0b\u63a8\u7406\uff1a<\/p>\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-k) = \\dfrac{(x-h)^2}{4f}<\/span><\/td>\n<td>; \u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> 4f(y-k) = (x-h)^2<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> 4fy-4fk = x^2 - 2hx + h^2<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> 4fy = x^2 - 2hx + h^2 + 4fk<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> y = \\dfrac{1}{4f}x^2 - \\dfrac{h}{2f}x + \\dfrac{h^2 + 4fk}{4f}<\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u5982\u679c\u5728\u6b64\u65b9\u7a0b\u4e2d\u505a\u51fa\u66ff\u6362 <span class=\"katex-eq\" data-katex-display=\"false\">a=\\dfrac{1}{4f},<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">b=-\\dfrac{2h}{4f}<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">c=\\dfrac{h^2 + 4fk}{4f},<\/span> \u90a3\u4e48\u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b\u5c31\u4f1a\u53d8\u4e3a\u6807\u51c6\u65b9\u7a0b\uff0c\u800c\u8fd9\u6b63\u662f<a href=\"https:\/\/toposuranos.com\/factorizacion-del-polinomio-cuadratico-y-2n-cuadratico\/\" rel=\"noopener\" target=\"_blank\">\u4e8c\u6b21\u591a\u9879\u5f0f<\/a>\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{y=ax^2 + bx + c}<\/span>\n","protected":false},"excerpt":{"rendered":"<p>\u629b\u7269\u7ebf\u65b9\u7a0b\uff1a\u5b9a\u4e49\u548c\u6027\u8d28 \u6458\u8981\uff1a \u672c\u8bfe\u7a0b\u63a2\u8ba8\u4e86\u629b\u7269\u7ebf\u65b9\u7a0b\u7684\u5b9a\u4e49\u548c\u63a8\u5bfc\uff0c\u7a81\u51fa\u5176\u4f5c\u4e3a\u5230\u7126\u70b9\u548c\u51c6\u7ebf\u7b49\u8ddd\u79bb\u7684\u70b9\u96c6\u5408\u7684\u8d77\u6e90\u3002\u5728\u6b64\u6982\u5ff5\u7684\u57fa\u7840\u4e0a\uff0c\u56de\u987e\u4e86\u8bf8\u5982\u7b1b\u5361\u5c14\u5e73\u9762\u4e2d\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u548c\u56fe\u5f62\u5e73\u79fb\u7b49\u5148\u524d\u7684\u6982\u5ff5\uff0c\u4ece\u800c\u5f15\u5165\u4e86\u629b\u7269\u7ebf\u7684\u57fa\u672c\u65b9\u7a0b\u53ca\u5176\u4e0e\u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u5173\u7cfb\u3002\u6700\u540e\uff0c\u63a8\u5bfc\u51fa\u4e86\u4efb\u610f\u9876\u70b9\u7684\u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b\uff0c\u5e76\u5c06\u5176\u8f6c\u5316\u4e3a\u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u6807\u51c6\u5f62\u5f0f\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5b8c\u6210\u672c\u8bfe\u7a0b\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u7406\u89e3\u629b\u7269\u7ebf\u7684\u51e0\u4f55\u5b9a\u4e49\uff0c\u4f5c\u4e3a\u5230\u7126\u70b9\u548c\u51c6\u7ebf\u7b49\u8ddd\u79bb\u7684\u70b9\u96c6\u5408\u3002 \u63a8\u5bfc\u629b\u7269\u7ebf\u7684\u57fa\u672c\u65b9\u7a0b\uff0c\u5229\u7528\u7126\u70b9-\u51c6\u7ebf\u7684\u8ddd\u79bb\u5173\u7cfb\u3002 \u7406\u89e3\u629b\u7269\u7ebf\u4e0e\u4e8c\u6b21\u591a\u9879\u5f0f\u4e4b\u95f4\u7684\u5173\u7cfb\u3002 \u63a8\u5bfc\u4efb\u610f\u9876\u70b9(h,k)\u7684\u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b\u3002 \u5185\u5bb9\u7d22\u5f15 \u629b\u7269\u7ebf\u65b9\u7a0b\u63a8\u5bfc\u7684\u5148\u524d\u6982\u5ff5 \u629b\u7269\u7ebf\u7684\u51e0\u4f55\u6982\u5ff5 \u7b1b\u5361\u5c14\u5e73\u9762\u4e2d\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb \u56fe\u5f62\u7684\u5e73\u79fb \u629b\u7269\u7ebf\u7684\u5b9a\u4e49 \u629b\u7269\u7ebf\u57fa\u672c\u65b9\u7a0b\u7684\u63a8\u5bfc \u629b\u7269\u7ebf\u7684\u901a\u7528\u65b9\u7a0b \u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\u4e0e\u4e8c\u6b21\u591a\u9879\u5f0f 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