{"id":28909,"date":"2021-04-23T13:00:38","date_gmt":"2021-04-23T13:00:38","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28909"},"modified":"2024-09-22T02:12:24","modified_gmt":"2024-09-22T02:12:24","slug":"%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d0%b5-%d0%bf%d0%b0%d1%80%d0%b0%d0%b1%d0%be%d0%bb-%d0%be%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d1%8f-%d0%b8-%d1%81%d0%b2%d0%be%d0%b9","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ru\/%d1%83%d1%80%d0%b0%d0%b2%d0%bd%d0%b5%d0%bd%d0%b8%d0%b5-%d0%bf%d0%b0%d1%80%d0%b0%d0%b1%d0%be%d0%bb-%d0%be%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d1%8f-%d0%b8-%d1%81%d0%b2%d0%be%d0%b9\/","title":{"rendered":"\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430<\/h1>\n<p><em><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><br \/>\n   \u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u0438\u0437\u0443\u0447\u0430\u044e\u0442\u0441\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u0432\u044b\u0432\u043e\u0434 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b, \u043f\u043e\u0434\u0447\u0435\u0440\u043a\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u0435\u0451 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u043a\u0430\u043a \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u0442\u043e\u0447\u0435\u043a, \u0440\u0430\u0432\u043d\u043e\u0443\u0434\u0430\u043b\u0451\u043d\u043d\u044b\u0445 \u043e\u0442 \u0444\u043e\u043a\u0443\u0441\u0430 \u0438 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b. \u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u043e\u0433\u043e \u043a\u043e\u043d\u0446\u0435\u043f\u0442\u0430 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043f\u0440\u0435\u0434\u0432\u0430\u0440\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u043d\u0430 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432, \u0447\u0442\u043e \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0432\u0432\u0435\u0441\u0442\u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b \u0438 \u0435\u0433\u043e \u0441\u0432\u044f\u0437\u044c \u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c\u0438 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430\u043c\u0438. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0441 \u0432\u0435\u0440\u0448\u0438\u043d\u043e\u0439 \u0432 \u043b\u044e\u0431\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0438 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442\u0441\u044f \u0432 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430.<br \/>\n   <\/em><\/p>\n<p><strong>\u0426\u0435\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f:<\/strong><br \/>\n   \u041a \u043a\u043e\u043d\u0446\u0443 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0443\u0447\u0430\u0449\u0438\u0439\u0441\u044f \u0441\u043c\u043e\u0436\u0435\u0442:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong> \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u043a\u0430\u043a \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u0442\u043e\u0447\u0435\u043a, \u0440\u0430\u0432\u043d\u043e\u0443\u0434\u0430\u043b\u0451\u043d\u043d\u044b\u0445 \u043e\u0442 \u0444\u043e\u043a\u0443\u0441\u0430 \u0438 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b.<\/li>\n<li><strong>\u0412\u044b\u0432\u0435\u0441\u0442\u0438<\/strong> \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0444\u043e\u043a\u0443\u0441\u043e\u043c \u0438 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u043e\u0439.<\/li>\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong> \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u043e\u0439 \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c\u0438 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430\u043c\u0438.<\/li>\n<li><strong>\u0412\u044b\u0432\u0435\u0441\u0442\u0438<\/strong> \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0441 \u0432\u0435\u0440\u0448\u0438\u043d\u043e\u0439 \u0432 \u043b\u044e\u0431\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 (h, k).<\/li>\n<\/ol>\n<p>   <strong>\u041e\u0433\u043b\u0430\u0432\u043b\u0435\u043d\u0438\u0435<\/strong><br \/>\n   <a href=\"#1\"><strong>\u041f\u0440\u0435\u0434\u0432\u0430\u0440\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0438\u0434\u0435\u0438 \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/strong><\/a><br \/>\n   <a href=\"#2\">\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/a><br \/>\n   <a href=\"#3\">\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u043d\u0430 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/a><br \/>\n   <a href=\"#4\">\u041f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432<\/a><br \/>\n   <a href=\"#5\"><strong>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/strong><\/a><br \/>\n   <a href=\"#6\">\u0412\u044b\u0432\u043e\u0434 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/a><br \/>\n   <a href=\"#7\">\u041e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/a><br \/>\n   <a href=\"#8\">\u041a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b<\/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=\"\u041f\u0440\u043e\u0438\u0433\u0440\u044b\u0432\u0430\u0442\u0435\u043b\u044c YouTube \u0432\u0438\u0434\u0435\u043e\" 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>\u041f\u0440\u0435\u0434\u0432\u0430\u0440\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0438\u0434\u0435\u0438 \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/h2>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=130s\" target=\"_blank\" rel=\"noopener\"><strong>\u041f\u0430\u0440\u0430\u0431\u043e\u043b\u0430 \u2014 \u044d\u0442\u043e \u043a\u0440\u0438\u0432\u0430\u044f<\/strong><\/a>, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442\u0441\u044f \u043a\u0430\u043a \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0432\u0441\u0435\u0445 \u0442\u043e\u0447\u0435\u043a, \u0440\u0430\u0432\u043d\u043e\u0443\u0434\u0430\u043b\u0451\u043d\u043d\u044b\u0445 \u043e\u0442 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438, \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0439 \u0444\u043e\u043a\u0443\u0441\u043e\u043c, \u0438 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439, \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0439 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u043e\u0439. \u0427\u0442\u043e\u0431\u044b \u043f\u043e\u043d\u044f\u0442\u044c \u044d\u0442\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u044c \u0435\u0433\u043e \u0432 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u044b\u043c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u043f\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0443\u0436\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0435\u0434\u0432\u0430\u0440\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u043f\u043e\u043d\u044f\u0442\u0438\u0439.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u043d\u0430 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=199s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0434\u0432\u0435 \u0442\u043e\u0447\u043a\u0438<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">p_1 = (x_1, y_1)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">p_2 = (x_2, y_2)<\/span>. \u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u044d\u0442\u0438\u043c\u0438 \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u2014 \u044d\u0442\u043e \u0434\u043b\u0438\u043d\u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0430, \u0441\u043e\u0435\u0434\u0438\u043d\u044f\u044e\u0449\u0435\u0433\u043e \u0438\u0445.<\/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=\"\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u0430\u043c\u0438\" 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=\"\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u0430\u043c\u0438\" class=\"aligncenter lazyload\" width=\"409\" height=\"263\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u041c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0437\u043c\u0435\u0440\u0438\u0442\u044c \u044d\u0442\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e <a href=\"https:\/\/youtu.be\/grjSzVl8Acw?t=553\" target=\"_blank\" rel=\"noopener\">\u0442\u0435\u043e\u0440\u0435\u043c\u044b \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430<\/a>, \u043a\u0430\u043a \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0434\u0438\u0430\u0433\u0440\u0430\u043c\u043c\u0435:<\/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=\"\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430\" 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=\"\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430\" class=\" aligncenter lazyload\" width=\"404\" height=\"255\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u0431\u0443\u0434\u0435\u0442:<\/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>\u041f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=390s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">y(x) = x^2<\/span>. \u0415\u0441\u043b\u0438 \u043c\u044b \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u043c \u0433\u0440\u0430\u0444\u0438\u043a, \u0442\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0447\u0442\u043e-\u0442\u043e \u0432\u0440\u043e\u0434\u0435 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043e \u043d\u0430 \u0440\u0438\u0441\u0443\u043d\u043a\u0435 \u043d\u0438\u0436\u0435:<\/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=\"\u041f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432\" 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=\"\u041f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432\" class=\" aligncenter lazyload\" width=\"325\" height=\"321\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0415\u0441\u043b\u0438 \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u043c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x-1<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">y-1<\/span>, \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430:<\/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=\"\u041f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432\" 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=\"\u041f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432\" class=\" aligncenter lazyload\" width=\"352\" height=\"288\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0412\u043e\u043e\u0431\u0449\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u043a\u0430\u0436\u0434\u043e\u0435 \u043f\u043e\u0434\u043e\u0431\u043d\u043e\u0435 \u0437\u0430\u043c\u0435\u0449\u0435\u043d\u0438\u0435 \u0432\u044b\u0437\u044b\u0432\u0430\u0435\u0442 \u043f\u0435\u0440\u0435\u043d\u043e\u0441, \u0430 \u0438\u043c\u0435\u043d\u043d\u043e:<\/p>\n<ul style=\"text-align: justify;\">\n<li><strong><span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto x-a<\/span>:<\/strong> \u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435, \u0433\u0440\u0430\u0444\u0438\u043a \u043f\u0435\u0440\u0435\u043c\u0435\u0449\u0430\u0435\u0442\u0441\u044f \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0435\u0434\u0438\u043d\u0438\u0446 \u0432\u043f\u0440\u0430\u0432\u043e, \u0435\u0441\u043b\u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u2014 \u0432\u043b\u0435\u0432\u043e.<\/li>\n<li><strong><span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto y-b<\/span>:<\/strong> \u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435, \u0433\u0440\u0430\u0444\u0438\u043a \u043f\u0435\u0440\u0435\u043c\u0435\u0449\u0430\u0435\u0442\u0441\u044f \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0435\u0434\u0438\u043d\u0438\u0446 \u0432\u0432\u0435\u0440\u0445, \u0435\u0441\u043b\u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u2014 \u0432\u043d\u0438\u0437.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u042d\u0442\u0438 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043f\u0435\u0440\u0435\u043d\u043e\u0441\u0430\u043c\u0438, \u0438 \u0438\u0445 \u043e\u0431\u0449\u0438\u0439 \u044d\u0444\u0444\u0435\u043a\u0442 \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u043e\u0431\u0449\u0438\u0442\u044c \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c \u0440\u0438\u0441\u0443\u043d\u043a\u0435:<\/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=\"\u041e\u0431\u0449\u0438\u0439 \u043f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432\" 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=\"\u041e\u0431\u0449\u0438\u0439 \u043f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432\" class=\"aligncenter lazyload\" width=\"522\" height=\"314\" \/><\/noscript><br \/>\n<a name=\"5\"><\/a><\/p>\n<h2>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/h2>\n<p style=\"text-align: justify;\">\u041f\u0430\u0440\u0430\u0431\u043e\u043b\u0430 \u2014 \u044d\u0442\u043e \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0432\u0441\u0435\u0445 \u0442\u043e\u0447\u0435\u043a, \u0440\u0430\u0432\u043d\u043e\u0443\u0434\u0430\u043b\u0451\u043d\u043d\u044b\u0445 \u043e\u0442 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0438 \u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439.<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=\"\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b\" 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=\"\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b\" class=\"aligncenter lazyload\" width=\"426\" height=\"302\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0424\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u0444\u043e\u043a\u0443\u0441\u043e\u043c<\/strong>, \u0430 \u043f\u0440\u044f\u043c\u0430\u044f \u2014 <strong>\u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u043e\u0439<\/strong>. \u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0441\u043d\u043e\u0432\u043e\u043f\u043e\u043b\u0430\u0433\u0430\u044e\u0449\u0438\u043c \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0431\u043e\u043b\u0435\u0435 \u0433\u043b\u0443\u0431\u043e\u043a\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c, \u043a\u0430\u043a \u0438\u0437\u043c\u0435\u0440\u044f\u0435\u0442\u0441\u044f \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043d\u0430 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043a\u0430\u043a \u0435\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438.<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u0412\u044b\u0432\u043e\u0434 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=604s\" target=\"_blank\" rel=\"noopener\"><strong>\u0414\u043b\u044f \u043f\u0440\u043e\u0441\u0442\u043e\u0442\u044b \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u0444\u043e\u043a\u0443\u0441<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">p_f= (0,f)<\/span>, \u0430 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u0430 \u0438\u043c\u0435\u0435\u0442 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">y=-p<\/span>.<\/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=\"\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b\" 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=\"\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b\" class=\" aligncenter lazyload\" width=\"334\" height=\"249\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0415\u0441\u043b\u0438 \u043c\u044b \u0432\u043e\u0437\u044c\u043c\u0435\u043c \u043b\u044e\u0431\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0441 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span>, \u0442\u043e \u043e\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u043d\u043e\u0443\u0434\u0430\u043b\u0435\u043d\u0430 \u043e\u0442 \u0444\u043e\u043a\u0443\u0441\u0430 \u0438 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b. \u042d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0438\u0441\u0430\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<p style=\"text-align: center;\">\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0444\u043e\u043a\u0443\u0441\u0430 \u0434\u043e \u0442\u043e\u0447\u043a\u0438(x,y) <span class=\"katex-eq\" data-katex-display=\"false\">= \\sqrt{x^2 + (f-y)^2}= y+f =<\/span> \u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438(x,y) \u0434\u043e \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b<\/p>\n<p style=\"text-align: justify;\">\u0418 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u043e\u0433\u043e \u0440\u0430\u0437\u0432\u043e\u0440\u0430\u0447\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0445\u043e\u0434 \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u0439:<\/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>; \u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \u0434\u043e \u0444\u043e\u043a\u0443\u0441\u0430 = \u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \u0434\u043e \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b, \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/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>; \u0418\u0437 (1), \u0432\u043e\u0437\u0432\u043e\u0434\u0438\u043c \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043e\u0431\u0435 \u0441\u0442\u043e\u0440\u043e\u043d\u044b<\/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;\">\u042d\u0442\u043e \u0438 \u0435\u0441\u0442\u044c \u0442\u043e, \u0447\u0442\u043e \u043c\u044b \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c <strong>\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/strong>.<\/p>\n<p style=\"text-align: justify;\">\u0415\u0441\u043b\u0438 \u0432\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u044d\u0442\u0443 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0443, \u043c\u043e\u0436\u043d\u043e \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u0447\u0442\u043e \u0432 \u043d\u0435\u0439 \u0435\u0441\u0442\u044c \u0442\u043e\u0447\u043a\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0431\u043b\u0438\u0436\u0430\u0439\u0448\u0435\u0439 \u043a \u0444\u043e\u043a\u0443\u0441\u0443 (\u0438\u043b\u0438, \u0447\u0442\u043e \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e, \u043a \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u0435). \u042d\u0442\u0430 \u0442\u043e\u0447\u043a\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u0432\u0435\u0440\u0448\u0438\u043d\u043e\u0439<\/strong>, \u0438 \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0435\u0451 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u2014 <span class=\"katex-eq\" data-katex-display=\"false\">(0,0)<\/span>; \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0444\u043e\u043a\u0443\u0441\u043e\u043c \u0438 \u0432\u0435\u0440\u0448\u0438\u043d\u043e\u0439 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u0444\u043e\u043a\u0443\u0441\u043d\u044b\u043c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435\u043c<\/strong>, \u0438 \u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043b\u044e\u0431\u044b\u043c \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c, \u043a\u0440\u043e\u043c\u0435 \u043d\u0443\u043b\u044f.<\/p>\n<p style=\"text-align: justify;\">\u041a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">f\\gt 0<\/span>, \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0430 \u043e\u0442\u043a\u0440\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0432\u0432\u0435\u0440\u0445, \u0430 \u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f\\lt 0<\/span>, \u0442\u043e \u0432\u043d\u0438\u0437. \u041a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">f\\to 0<\/span>, \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0430 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0439, \u0432\u0435\u0440\u0448\u0438\u043d\u0430 \u043e\u0441\u0442\u0430\u0451\u0442\u0441\u044f \u043d\u0430 \u0441\u0432\u043e\u0451\u043c \u043c\u0435\u0441\u0442\u0435, \u0430 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u0430 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a \u0432\u0435\u0440\u0448\u0438\u043d\u0435. \u0412\u0438\u0437\u0443\u0430\u043b\u044c\u043d\u043e \u044d\u0442\u043e \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0442\u0430\u043a, \u043a\u0430\u043a \u0431\u0443\u0434\u0442\u043e \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0430 \u0438 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u0430 \u0441\u043b\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u0432 \u043e\u0434\u043d\u0443 \u043b\u0438\u043d\u0438\u044e; \u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e, \u0433\u0440\u0430\u0444\u0438\u043a \u0438\u0441\u0447\u0435\u0437\u0430\u0435\u0442, \u0442\u0430\u043a \u043a\u0430\u043a \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043d\u0430 \u043d\u043e\u043b\u044c \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e.<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u041e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=1007s\" target=\"_blank\" rel=\"noopener\"><strong>\u0418\u0437 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/strong><\/a> \u0438 \u043f\u0435\u0440\u0435\u043d\u043e\u0441\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432, \u0437\u0430\u043c\u0435\u043d\u044f\u044f <span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto (x-h)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto (y-k),<\/span> \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c <strong>\u041e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/strong> \u0441 \u0432\u0435\u0440\u0448\u0438\u043d\u043e\u0439 \u0432 \u0442\u043e\u0447\u043a\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">(h,k)<\/span>.<\/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>\u041a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=1116s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0430\u0437\u0432\u0438\u0432\u0430\u044f \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/strong><\/a>, \u043c\u044b \u043f\u0440\u0438\u0445\u043e\u0434\u0438\u043c \u043a \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u0445\u043e\u0434\u0443 \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u0439:<\/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>; \u041e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b<\/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;\">\u0415\u0441\u043b\u0438 \u0432 \u044d\u0442\u043e\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0437\u0430\u043c\u0435\u043d\u044b <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> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">c=\\dfrac{h^2 + 4fk}{4f},<\/span> \u0442\u043e\u0433\u0434\u0430 \u043e\u0431\u0449\u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442\u0441\u044f \u0432 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043f\u043e \u0441\u0443\u0442\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <a href=\"https:\/\/toposuranos.com\/factorizacion-del-polinomio-cuadratico-y-2n-cuadratico\/\" rel=\"noopener\" target=\"_blank\">\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u043c<\/a>.<\/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>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0420\u0435\u0437\u044e\u043c\u0435: \u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u0438\u0437\u0443\u0447\u0430\u044e\u0442\u0441\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u0432\u044b\u0432\u043e\u0434 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b, \u043f\u043e\u0434\u0447\u0435\u0440\u043a\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u0435\u0451 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u043a\u0430\u043a \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u0442\u043e\u0447\u0435\u043a, \u0440\u0430\u0432\u043d\u043e\u0443\u0434\u0430\u043b\u0451\u043d\u043d\u044b\u0445 \u043e\u0442 \u0444\u043e\u043a\u0443\u0441\u0430 \u0438 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u044b. \u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u043e\u0433\u043e \u043a\u043e\u043d\u0446\u0435\u043f\u0442\u0430 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043f\u0440\u0435\u0434\u0432\u0430\u0440\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0442\u043e\u0447\u043a\u0430\u043c\u0438 \u043d\u0430 \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0438 \u043f\u0435\u0440\u0435\u043d\u043e\u0441 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432, \u0447\u0442\u043e \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0432\u0432\u0435\u0441\u0442\u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b \u0438 \u0435\u0433\u043e \u0441\u0432\u044f\u0437\u044c \u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c\u0438 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28890,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":101,"footnotes":""},"categories":[589,573],"tags":[],"class_list":["post-28909","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-589","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u0431\u043e\u043b: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 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