{"id":28907,"date":"2021-04-23T13:00:39","date_gmt":"2021-04-23T13:00:39","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28907"},"modified":"2024-09-22T02:11:53","modified_gmt":"2024-09-22T02:11:53","slug":"%e0%a4%aa%e0%a4%b0%e0%a4%b5%e0%a4%b2%e0%a4%af-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%ad%e0%a4%be%e0%a4%b7%e0%a4%be%e0%a4%8f%e0%a4%81-%e0%a4%94","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%aa%e0%a4%b0%e0%a4%b5%e0%a4%b2%e0%a4%af-%e0%a4%b8%e0%a4%ae%e0%a5%80%e0%a4%95%e0%a4%b0%e0%a4%a3-%e0%a4%aa%e0%a4%b0%e0%a4%bf%e0%a4%ad%e0%a4%be%e0%a4%b7%e0%a4%be%e0%a4%8f%e0%a4%81-%e0%a4%94\/","title":{"rendered":"\u092a\u0930\u0935\u0932\u092f \u0938\u092e\u0940\u0915\u0930\u0923: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901 \u0914\u0930 \u0917\u0941\u0923"},"content":{"rendered":"<p><center><\/p>\n<h1>\u092a\u0930\u0935\u0932\u092f \u0938\u092e\u0940\u0915\u0930\u0923: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901 \u0914\u0930 \u0917\u0941\u0923<\/h1>\n<p><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n   \u092f\u0939 \u0915\u0915\u094d\u0937\u093e \u092a\u0930\u0935\u0932\u092f \u0915\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0914\u0930 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0924\u094d\u0924\u093f \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u0924\u0940 \u0939\u0948, \u091c\u094b \u0907\u0938\u0947 \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0947\u0916\u093e \u0938\u0947 \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u0938\u0947\u091f \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u092a\u0942\u0930\u094d\u0935 \u0915\u0940 \u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u091c\u0948\u0938\u0947 \u0915\u093f \u0915\u093e\u0930\u094d\u091f\u0947\u0936\u093f\u092f\u0928 \u0938\u092e\u0924\u0932 \u092e\u0947\u0902 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u093c \u0915\u093e \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923, \u091c\u094b \u0939\u092e\u0947\u0902 \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u092e\u094c\u0932\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0907\u0938\u0915\u093e \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0905\u0902\u0924 \u092e\u0947\u0902, \u0915\u093f\u0938\u0940 \u092d\u0940 \u092c\u093f\u0902\u0926\u0941 (h,k) \u092a\u0930 \u0936\u0940\u0930\u094d\u0937 \u0935\u093e\u0932\u0947 \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0907\u0938\u0947 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926 \u0915\u0947 \u092e\u093e\u0928\u0915 \u0930\u0942\u092a \u092e\u0947\u0902 \u092c\u0926\u0932 \u0926\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<br \/>\n   <\/em><\/p>\n<p><strong>\u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f:<\/strong><br \/>\n   \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u0924\u0915, \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0915\u093f \u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u090f\u0915 \u0930\u0947\u0916\u093e \u0938\u0947 \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u093e \u0938\u0947\u091f \u0939\u0948\u0964<\/li>\n<li><strong>\u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u0930\u0947\u0902<\/strong> \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u092e\u094c\u0932\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923, \u092b\u094b\u0915\u0938-\u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u0915\u093f \u092a\u0930\u0935\u0932\u092f \u0914\u0930 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u094d\u092f\u093e \u0938\u0902\u092c\u0902\u0927 \u0939\u0948\u0964<\/li>\n<li><strong>\u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u0930\u0947\u0902<\/strong> \u0915\u093f\u0938\u0940 \u092d\u0940 \u092c\u093f\u0902\u0926\u0941 (h,k) \u092a\u0930 \u0936\u0940\u0930\u094d\u0937 \u0935\u093e\u0932\u0947 \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923\u0964<\/li>\n<\/ol>\n<p>   <strong>\u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0915\u0940 \u0938\u0942\u091a\u0940<\/strong><br \/>\n   <a href=\"#1\"><strong>\u092a\u0930\u0935\u0932\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u0935\u093f\u091a\u093e\u0930<\/strong><\/a><br \/>\n   <a href=\"#2\">\u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0927\u093e\u0930\u0923\u093e<\/a><br \/>\n   <a href=\"#3\">\u0915\u093e\u0930\u094d\u091f\u0947\u0936\u093f\u092f\u0928 \u0938\u092e\u0924\u0932 \u092e\u0947\u0902 \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940<\/a><br \/>\n   <a href=\"#4\">\u0917\u094d\u0930\u093e\u092b \u0915\u093e \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923<\/a><br \/>\n   <a href=\"#5\"><strong>\u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/strong><\/a><br \/>\n   <a href=\"#6\">\u092a\u0930\u0935\u0932\u092f \u0915\u0947 \u092e\u094c\u0932\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0924\u094d\u0924\u093f<\/a><br \/>\n   <a href=\"#7\">\u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/a><br \/>\n   <a href=\"#8\">\u092a\u0930\u0935\u0932\u092f \u0915\u093e \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926<\/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 \u0935\u0940\u0921\u093f\u092f\u094b \u092a\u094d\u0932\u0947\u092f\u0930\" 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>\u092a\u0930\u0935\u0932\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u0935\u093f\u091a\u093e\u0930<\/h2>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u0927\u093e\u0930\u0923\u093e<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=130s\" target=\"_blank\" rel=\"noopener\"><strong>\u092a\u0930\u0935\u0932\u092f \u090f\u0915 \u0935\u0915\u094d\u0930 \u0939\u0948<\/strong><\/a> \u091c\u094b \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092c\u093f\u0902\u0926\u0941 (\u091c\u093f\u0938\u0947 \u092b\u094b\u0915\u0938 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948) \u0914\u0930 \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0947\u0916\u093e (\u091c\u093f\u0938\u0947 \u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948) \u0938\u0947 \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u093e \u0938\u092e\u0942\u0939 \u0939\u0948\u0964 \u0907\u0938 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0914\u0930 \u0907\u0938\u0947 \u090f\u0915 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u092e\u0947\u0902 \u092c\u0926\u0932\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u091c\u093f\u0938\u0947 \u0939\u092e \u0938\u0902\u091a\u093e\u0932\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923, \u092a\u0939\u0932\u0947 \u0939\u092e\u0947\u0902 \u0915\u0941\u091b \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0915\u093e\u0930\u094d\u091f\u0947\u0936\u093f\u092f\u0928 \u0938\u092e\u0924\u0932 \u092e\u0947\u0902 \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=199s\" target=\"_blank\" rel=\"noopener\"><strong>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0926\u094b \u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">p_1 = (x_1, y_1)<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">p_2 = (x_2, y_2)<\/span>\u0964 \u0907\u0928 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 \u0935\u0939 \u0930\u0947\u0916\u093e \u0916\u0902\u0921 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 \u0939\u0948 \u091c\u094b \u0909\u0928\u094d\u0939\u0947\u0902 \u091c\u094b\u0921\u093c\u0924\u0940 \u0939\u0948\u0964<\/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=\"\u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940\" 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=\"\u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940\" class=\"aligncenter lazyload\" width=\"409\" height=\"263\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0939\u092e \u0907\u0938 \u0926\u0942\u0930\u0940 \u0915\u094b <a href=\"https:\/\/youtu.be\/grjSzVl8Acw?t=553\" target=\"_blank\" rel=\"noopener\">\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u092a\u094d\u0930\u092e\u0947\u092f<\/a> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092e\u093e\u092a \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/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=\"\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u092a\u094d\u0930\u092e\u0947\u092f\" 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=\"\u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u092a\u094d\u0930\u092e\u0947\u092f\" class=\" aligncenter lazyload\" width=\"404\" height=\"255\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u0939\u094b\u0917\u0940:<\/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>\u0917\u094d\u0930\u093e\u092b \u0915\u093e \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=390s\" target=\"_blank\" rel=\"noopener\"><strong>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0915\u094b\u0908 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0939\u0948<\/strong><\/a><span class=\"katex-eq\" data-katex-display=\"false\">y(x) = x^2<\/span>\u0964 \u092f\u0926\u093f \u0939\u092e \u0907\u0938\u0947 \u0917\u094d\u0930\u093e\u092b\u093c \u0915\u0930\u0947\u0902\u0917\u0947, \u0924\u094b \u0939\u092e\u0947\u0902 \u0928\u0940\u091a\u0947 \u0926\u093f\u090f \u0917\u090f \u091a\u093f\u0924\u094d\u0930 \u091c\u0948\u0938\u093e \u0915\u0941\u091b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0917\u093e:<\/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=\"\u0917\u094d\u0930\u093e\u092b \u0915\u093e \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923\" 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=\"\u0917\u094d\u0930\u093e\u092b \u0915\u093e \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923\" class=\" aligncenter lazyload\" width=\"325\" height=\"321\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u092f\u0926\u093f \u0939\u092e \u0907\u0938 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u094b <span class=\"katex-eq\" data-katex-display=\"false\">x-1<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u0915\u094b <span class=\"katex-eq\" data-katex-display=\"false\">y-1<\/span> \u0938\u0947 \u092c\u0926\u0932\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u0917\u094d\u0930\u093e\u092b\u093c \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0926\u0947\u0916\u0947\u0902\u0917\u0947:<\/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=\"\u0917\u094d\u0930\u093e\u092b \u0915\u093e \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923\" 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=\"\u0917\u094d\u0930\u093e\u092b \u0915\u093e \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923\" class=\" aligncenter lazyload\" width=\"352\" height=\"288\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u0938\u0947, \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0938\u0947 \u090f\u0915 \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0939\u094b\u0924\u093e \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924\u094d:<\/p>\n<ul style=\"text-align: justify;\">\n<li><strong><span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto x-a<\/span>:<\/strong> \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u0948, \u0924\u094b \u092f\u0939 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0907\u0915\u093e\u0907\u092f\u094b\u0902 \u0938\u0947 \u0926\u093e\u0908\u0902 \u0913\u0930 \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u093f\u0924 \u0939\u094b\u0917\u093e, \u0914\u0930 \u092f\u0926\u093f \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u0948, \u0924\u094b \u092c\u093e\u0908\u0902 \u0913\u0930\u0964<\/li>\n<li><strong><span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto y-b<\/span>:<\/strong> \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u0948, \u0924\u094b \u092f\u0939 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0907\u0915\u093e\u0907\u092f\u094b\u0902 \u0938\u0947 \u090a\u092a\u0930 \u0915\u0940 \u0913\u0930 \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u093f\u0924 \u0939\u094b\u0917\u093e, \u0914\u0930 \u092f\u0926\u093f \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0939\u0948, \u0924\u094b \u0928\u0940\u091a\u0947\u0964<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u092f\u0947 \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0939\u0948\u0902, \u0914\u0930 \u0907\u0928\u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u092a\u094d\u0930\u092d\u093e\u0935 \u0928\u0940\u091a\u0947 \u0926\u0940 \u0917\u0908 \u0906\u0915\u0943\u0924\u093f \u092e\u0947\u0902 \u0938\u0902\u0915\u094d\u0937\u0947\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948:<\/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=\"\u0917\u094d\u0930\u093e\u092b \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923\" 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=\"\u0917\u094d\u0930\u093e\u092b \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923\" class=\"aligncenter lazyload\" width=\"522\" height=\"314\" \/><\/noscript><br \/>\n<a name=\"5\"><\/a><\/p>\n<h2>\u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/h2>\n<p style=\"text-align: justify;\">\u092a\u0930\u0935\u0932\u092f \u0935\u0939 \u092c\u093f\u0902\u0926\u0941 \u0938\u0947\u091f \u0939\u0948 \u091c\u094b \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0947\u0916\u093e \u0938\u0947 \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<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=\"\u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e\" 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=\"\u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e\" class=\"aligncenter lazyload\" width=\"426\" height=\"302\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092c\u093f\u0902\u0926\u0941 \u0915\u094b <strong>\u092b\u094b\u0915\u0938<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0930\u0947\u0916\u093e \u0915\u094b <strong>\u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u0926\u0942\u0930\u0940 \u0915\u0940 \u0927\u093e\u0930\u0923\u093e \u092a\u0930\u0935\u0932\u092f \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092e\u094c\u0932\u093f\u0915 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u0917\u0939\u0928 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e\u0947\u0902 \u092a\u0941\u0928\u0903 \u092f\u0939 \u0926\u0947\u0916\u0928\u093e \u0939\u094b\u0917\u093e \u0915\u093f \u0915\u093e\u0930\u094d\u091f\u0947\u0936\u093f\u092f\u0928 \u0938\u092e\u0924\u0932 \u092a\u0930 \u0926\u0942\u0930\u0940 \u0915\u0948\u0938\u0947 \u092e\u093e\u092a\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u092e\u0947\u0902 \u0915\u0948\u0938\u0947 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u092a\u0930\u0935\u0932\u092f \u0915\u0947 \u092e\u094c\u0932\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0924\u094d\u0924\u093f<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=604s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u0930\u0932\u0924\u093e \u0915\u0947 \u0932\u093f\u090f, \u092e\u093e\u0928 \u0932\u0947\u0902 \u092b\u094b\u0915\u0932 \u092c\u093f\u0902\u0926\u0941<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">p_f= (0,f)<\/span> \u0914\u0930 \u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 <span class=\"katex-eq\" data-katex-display=\"false\">y=-p<\/span> \u0939\u0948\u0964<\/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=\"\u092a\u0930\u0935\u0932\u092f \u0938\u092e\u0940\u0915\u0930\u0923\" 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=\"\u092a\u0930\u0935\u0932\u092f \u0938\u092e\u0940\u0915\u0930\u0923\" class=\" aligncenter lazyload\" width=\"334\" height=\"249\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u092f\u0926\u093f \u0939\u092e \u092a\u0930\u0935\u0932\u092f \u092a\u0930 \u0915\u093f\u0938\u0940 \u092c\u093f\u0902\u0926\u0941 \u0915\u094b <span class=\"katex-eq\" data-katex-display=\"false\">(x,y)<\/span> \u092a\u0930 \u0932\u0947\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092f\u0939 \u092c\u093f\u0902\u0926\u0941 \u092b\u094b\u0915\u0938 \u0914\u0930 \u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0938\u0947 \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0939\u094b\u0917\u093e\u0964 \u0907\u0938\u0947 \u0939\u092e \u0928\u093f\u092e\u094d\u0928 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align: center;\">\u092b\u094b\u0915\u0938-\u092c\u093f\u0902\u0926\u0941 \u0926\u0942\u0930\u0940 <span class=\"katex-eq\" data-katex-display=\"false\">= \\sqrt{x^2 + (f-y)^2}= y+f =<\/span> \u092c\u093f\u0902\u0926\u0941-\u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0926\u0942\u0930\u0940<\/p>\n<p style=\"text-align: justify;\">\u0914\u0930 \u0907\u0938 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0928\u093f\u092e\u094d\u0928 \u0924\u0930\u094d\u0915 \u0935\u093f\u0915\u0938\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/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>; \u092c\u093f\u0902\u0926\u0941-\u092b\u094b\u0915\u0938 \u0926\u0942\u0930\u0940 = \u092c\u093f\u0902\u0926\u0941-\u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0926\u0942\u0930\u0940, \u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/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>; (1) \u0938\u0947, \u0926\u094b\u0928\u094b\u0902 \u092a\u0915\u094d\u0937\u094b\u0902 \u0915\u093e \u0935\u0930\u094d\u0917<\/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;\">\u092f\u0939 \u0905\u0902\u0924\u093f\u092e \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u0930\u0935\u0932\u092f \u0915\u093e <strong>\u092e\u094c\u0932\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923<\/strong> \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u092f\u0926\u093f \u0939\u092e \u0907\u0938 \u092a\u0930\u0935\u0932\u092f \u0915\u094b \u0927\u094d\u092f\u093e\u0928 \u0938\u0947 \u0926\u0947\u0916\u0947\u0902, \u0924\u094b \u0939\u092e \u092a\u093e\u090f\u0902\u0917\u0947 \u0915\u093f \u0907\u0938\u092e\u0947\u0902 \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0910\u0938\u093e \u0939\u0948 \u091c\u094b \u092b\u094b\u0915\u0938 (\u092f\u093e \u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938) \u0915\u0947 \u0938\u092c\u0938\u0947 \u0928\u093f\u0915\u091f \u0939\u0948\u0964 \u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u0915\u094b <strong>\u0936\u0940\u0930\u094d\u0937<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0907\u0938 \u0935\u093f\u0936\u0947\u0937 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902 \u0907\u0938\u0915\u0940 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">(0,0)<\/span> \u0939\u094b\u0924\u0940 \u0939\u0948; \u092b\u094b\u0915\u0938 \u0914\u0930 \u0936\u0940\u0930\u094d\u0937 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 \u0915\u094b <strong>\u092b\u094b\u0915\u0932 \u0926\u0942\u0930\u0940<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u0907\u0938\u0915\u093e \u092e\u093e\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0915\u094b\u0908 \u092d\u0940 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948 \u0938\u093f\u0935\u093e\u092f \u0936\u0942\u0928\u094d\u092f \u0915\u0947\u0964<\/p>\n<p style=\"text-align: justify;\">\u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">f\\gt 0<\/span> \u0939\u094b, \u0924\u094b \u092a\u0930\u0935\u0932\u092f \u090a\u092a\u0930 \u0915\u0940 \u0913\u0930 \u0916\u0941\u0932\u0924\u093e \u0939\u0948, \u0914\u0930 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">f\\lt 0<\/span> \u0939\u094b, \u0924\u094b \u0928\u0940\u091a\u0947 \u0915\u0940 \u0913\u0930 \u0916\u0941\u0932\u0924\u093e \u0939\u0948\u0964 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">f\\to 0<\/span>, \u092a\u0930\u0935\u0932\u092f \u0938\u092e\u0924\u0932 \u0939\u094b\u0924\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u092c\u0915\u093f \u0936\u0940\u0930\u094d\u0937 \u0905\u092a\u0928\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u092c\u0928\u093e\u090f \u0930\u0916\u0924\u093e \u0939\u0948, \u0914\u0930 \u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u0936\u0940\u0930\u094d\u0937 \u0915\u0947 \u0915\u0930\u0940\u092c \u0906\u0924\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0910\u0938\u093e \u092a\u094d\u0930\u0924\u0940\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u0948\u0938\u0947 \u092a\u0930\u0935\u0932\u092f \u0914\u0930 \u0921\u093e\u092f\u0930\u0947\u0915\u094d\u091f\u094d\u0930\u093f\u0915\u094d\u0938 \u090f\u0915 \u0939\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u092e\u093f\u0932 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902; \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u0917\u094d\u0930\u093e\u092b \u0917\u093e\u092f\u092c \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0936\u0942\u0928\u094d\u092f \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u0928 \u0938\u0902\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e\u0964<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=1007s\" target=\"_blank\" rel=\"noopener\"><strong>\u092a\u0930\u0935\u0932\u092f \u0915\u0947 \u092e\u094c\u0932\u093f\u0915 \u0938\u092e\u0940\u0915\u0930\u0923<\/strong><\/a> \u0914\u0930 \u0917\u094d\u0930\u093e\u092b \u0938\u094d\u0925\u093e\u0928\u093e\u0902\u0924\u0930\u0923 \u0938\u0947 \u0939\u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">x\\longmapsto (x-h)<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">y\\longmapsto (y-k)<\/span> \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a <span class=\"katex-eq\" data-katex-display=\"false\">(h,k)<\/span> \u0936\u0940\u0930\u094d\u0937 \u0935\u093e\u0932\u0947 \u092a\u0930\u0935\u0932\u092f \u0915\u093e <strong>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/strong> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/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>\u092a\u0930\u0935\u0932\u092f \u0915\u093e \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=O2EYxxK03jU&amp;t=1116s\" target=\"_blank\" rel=\"noopener\"><strong>\u092f\u0926\u093f \u0939\u092e \u092a\u0930\u0935\u0932\u092f \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0935\u093f\u0915\u093e\u0938 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902<\/strong><\/a>, \u0924\u094b \u0939\u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u094d\u0915 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/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>; \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923<\/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;\">\u092f\u0926\u093f \u0939\u092e \u0907\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 <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> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">c=\\dfrac{h^2 + 4fk}{4f}<\/span> \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 \u092c\u0926\u0932 \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u094b \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 <a href=\"https:\/\/toposuranos.com\/factorizacion-del-polinomio-cuadratico-y-2n-cuadratico\/\" rel=\"noopener\" target=\"_blank\">\u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926<\/a> \u0939\u0948\u0964<\/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>\u092a\u0930\u0935\u0932\u092f \u0938\u092e\u0940\u0915\u0930\u0923: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901 \u0914\u0930 \u0917\u0941\u0923 \u0938\u093e\u0930\u093e\u0902\u0936: \u092f\u0939 \u0915\u0915\u094d\u0937\u093e \u092a\u0930\u0935\u0932\u092f \u0915\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0914\u0930 \u0935\u094d\u092f\u0941\u0924\u094d\u092a\u0924\u094d\u0924\u093f \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u0924\u0940 \u0939\u0948, \u091c\u094b \u0907\u0938\u0947 \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0947\u0916\u093e \u0938\u0947 \u0938\u092e\u093e\u0928 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0938\u094d\u0925\u093f\u0924 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u0938\u0947\u091f \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u092a\u0942\u0930\u094d\u0935 \u0915\u0940 \u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u091c\u093e\u0924\u0940 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