{"id":28937,"date":"2021-04-27T13:00:19","date_gmt":"2021-04-27T13:00:19","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28937"},"modified":"2024-09-22T02:16:05","modified_gmt":"2024-09-22T02:16:05","slug":"%e0%a4%aa%e0%a4%b0%e0%a4%b5%e0%a4%b2%e0%a4%af-%e0%a4%94%e0%a4%b0-%e0%a4%89%e0%a4%a8%e0%a4%95%e0%a5%87-%e0%a4%97%e0%a5%8d%e0%a4%b0%e0%a4%be%e0%a4%ab%e0%a4%bc-%e0%a4%95%e0%a5%80-%e0%a4%b5%e0%a4%bf","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%94%e0%a4%b0-%e0%a4%89%e0%a4%a8%e0%a4%95%e0%a5%87-%e0%a4%97%e0%a5%8d%e0%a4%b0%e0%a4%be%e0%a4%ab%e0%a4%bc-%e0%a4%95%e0%a5%80-%e0%a4%b5%e0%a4%bf\/","title":{"rendered":"\u092a\u0930\u0935\u0932\u092f \u0914\u0930 \u0909\u0928\u0915\u0947 \u0917\u094d\u0930\u093e\u092b\u093c \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901"},"content":{"rendered":"<p><center><\/p>\n<h1>\u092a\u0930\u0935\u0932\u092f \u0914\u0930 \u0909\u0928\u0915\u0947 \u0917\u094d\u0930\u093e\u092b\u093c \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901<\/h1>\n<p><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n   \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u0913\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u0909\u0928\u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u092e\u093e\u0928\u0915 \u0930\u0942\u092a \u0938\u0947, \u092f\u0939 \u0938\u092e\u091d\u093e\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u0915\u0948\u0938\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0924\u0924\u094d\u0935\u094b\u0902 \u091c\u0948\u0938\u0947 \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938, \u092b\u094b\u0915\u0938, \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0930\u0947\u0916\u093e, \u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0927\u0941\u0930\u0940, \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 x-\u0905\u0915\u094d\u0937 \u0915\u0947 \u0915\u091f\u093e\u0935\u094b\u0902 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0940 \u091c\u093e\u090f\u0964<br \/>\n   <\/em><br \/>\n   <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 \u092e\u0947\u0902 \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0917\u093e<\/p>\n<ol style=\"text-align: left;\">\n<li><strong>\u0917\u0923\u0928\u093e<\/strong> \u0915\u0930\u0947\u0902 \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938, \u092b\u094b\u0915\u0938 \u0914\u0930 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0930\u0947\u0916\u093e \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0930\u0942\u092a \u0938\u0947\u0964<\/li>\n<li><strong>\u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924<\/strong> \u0915\u0930\u0947\u0902 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u092e\u0947\u0902 \u091c\u094d\u092f\u093e\u092e\u093f\u0924\u0940\u092f \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f\u0964<\/li>\n<li><strong>\u0930\u0942\u092a\u0930\u0947\u0916\u093e<\/strong> \u0924\u0948\u092f\u093e\u0930 \u0915\u0930\u0947\u0902 \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0917\u094d\u0930\u093e\u092b\u093c \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930\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\">\u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0930\u0942\u092a<\/a><br \/>\n   <a href=\"#2\">\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947 \u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901<\/a><br \/>\n   <a href=\"#3\">\u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947 \u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901<\/a><br \/>\n   <a href=\"#4\">Excel \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u094d\u0935\u091a\u093e\u0932\u093f\u0924 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923<\/a>\n   <\/p>\n<p>   <\/center><br \/>\n   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/C6DbrJDiZTM\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n   <a name=\"1\"><\/a><\/p>\n<h2>\u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0930\u0942\u092a<\/h2>\n<p style=\"text-align: justify;\">\u092a\u093f\u091b\u0932\u0940 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e\u0928\u0947 \u0926\u0947\u0916\u093e \u0915\u093f \u092a\u0930\u0935\u0932\u092f \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x-x_0)^2 =4f(y-y_0)<\/span>\n<p style=\"text-align: justify;\">\u091c\u0939\u093e\u0902 \u092f\u0941\u0917\u094d\u092e <span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0)<\/span> \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0939\u0948 \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u092b\u094b\u0915\u0932 \u0926\u0942\u0930\u0940 \u0939\u0948\u0964 \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f \\gt 0<\/span> \u0939\u0948, \u0924\u094b \u092b\u094b\u0915\u0938 \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938 \u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0926\u0942\u0930\u0940 \u092a\u0930 \u0939\u094b\u0924\u093e \u0939\u0948, \u0914\u0930 \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f \\lt 0<\/span> \u0939\u0948, \u0924\u094b \u092b\u094b\u0915\u0938 \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938 \u0915\u0947 \u0928\u0940\u091a\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0926\u0942\u0930\u0940 \u092a\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0939\u092e\u0928\u0947 \u092f\u0939 \u092d\u0940 \u0926\u0947\u0916\u093e \u0915\u093f \u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u093e\u0928\u0915 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0936\u094d\u0930\u0947\u0923\u0940 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0964<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y(x) = ax^2 + bx + c,<\/span> \u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">a \\neq 0<\/span>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=228s\" target=\"_blank\" rel=\"noopener\"><strong>\u090f\u0915 \u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e<\/strong><\/a> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u094b \u0909\u091c\u093e\u0917\u0930 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0939\u0948\u0964<\/p>\n<ul style=\"text-align: justify;\">\n<li>\u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938 \u0915\u0947 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915<\/li>\n<li>\u092b\u094b\u0915\u0938 \u0915\u0947 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915<\/li>\n<li>\u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0930\u0947\u0916\u093e \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923<\/li>\n<li>\u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0927\u0941\u0930\u0940 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923<\/li>\n<li>x-\u0905\u0915\u094d\u0937 \u0915\u0947 \u0915\u091f\u093e\u0935 (\u092f\u0926\u093f \u092e\u094c\u091c\u0942\u0926 \u0939\u094b\u0902)<\/li>\n<li>\u0905\u0902\u0924 \u092e\u0947\u0902, \u090f\u0915 \u0938\u094d\u0915\u0947\u091a \u092c\u0928\u093e\u090f\u0902 \u090f\u0915\u0924\u094d\u0930\u093f\u0924 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930\u0964<\/li>\n<\/ul>\n<p>   <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-xAUdvfTRbjw\/YIbmIXDdT-I\/AAAAAAAAFAI\/8NH0t_EWbH0KIuFDnsRu2IyHdyN4WU54wCLcBGAsYHQ\/s0\/caracterizaci%25C3%25B3n%2Bde%2Bpar%25C3%25A1bolas.PNG\" alt=\"\u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901\" class=\" aligncenter lazyload\" width=\"537\" height=\"414\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-xAUdvfTRbjw\/YIbmIXDdT-I\/AAAAAAAAFAI\/8NH0t_EWbH0KIuFDnsRu2IyHdyN4WU54wCLcBGAsYHQ\/s0\/caracterizaci%25C3%25B3n%2Bde%2Bpar%25C3%25A1bolas.PNG\" alt=\"\u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901\" class=\" aligncenter lazyload\" width=\"537\" height=\"414\" \/><\/noscript><br \/>\n   <a name=\"2\"><\/a><\/p>\n<h2>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947 \u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=316s\" target=\"_blank\" rel=\"noopener\"><strong>\u092f\u0926\u093f \u0906\u092a\u0915\u0947 \u092a\u093e\u0938 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u0930\u0935\u0932\u092f \u0935\u0930\u094d\u0923\u093f\u0924 \u0939\u0948<\/strong><\/a>, \u0924\u094b \u0906\u092a\u0915\u0947 \u092a\u093e\u0938 \u092a\u0939\u0932\u0947 \u0938\u0947 \u0939\u0940 \u0905\u0927\u093f\u0915\u093e\u0902\u0936 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0939\u0948, \u0915\u0947\u0935\u0932 x-\u0905\u0915\u094d\u0937 \u0915\u0947 \u0915\u091f\u093e\u0935 \u0915\u094b \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0917\u0940\u0964<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x-x_0)^2 =4f(y-y_0)<\/span>\n<p style=\"text-align: justify;\">\u092f\u0939\u093e\u0902 \u0938\u0947 \u0906\u092a\u0915\u0947 \u092a\u093e\u0938 \u0939\u0948:<\/p>\n<ul style=\"text-align: justify;\">\n<li><strong>\u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938:<\/strong> \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0)<\/span><\/li>\n<li><strong>\u092b\u094b\u0915\u0938 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f:<\/strong> \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938 \u0915\u0947 \u090a\u092a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0907\u0915\u093e\u0907\u092f\u094b\u0902 \u092a\u0930<\/li>\n<li><strong>\u092b\u094b\u0915\u0938:<\/strong> \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0 + f)<\/span><\/li>\n<li><strong>\u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0930\u0947\u0916\u093e:<\/strong> \u0938\u092e\u0940\u0915\u0930\u0923 <span class=\"katex-eq\" data-katex-display=\"false\">y = y_0 - f<\/span><\/li>\n<li><strong>\u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0927\u0941\u0930\u0940:<\/strong> \u0938\u092e\u0940\u0915\u0930\u0923 <span class=\"katex-eq\" data-katex-display=\"false\">x = x_0<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">x-\u0905\u0915\u094d\u0937 \u0915\u0947 \u0915\u091f\u093e\u0935 \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0906\u092a\u0915\u094b \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u094b \u092e\u093e\u0928\u0915 \u0930\u0942\u092a \u092e\u0947\u0902 \u092c\u0926\u0932\u0928\u093e \u0939\u094b\u0917\u093e, \u0914\u0930 \u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0936\u094d\u0930\u0947\u0923\u0940 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926 \u0915\u094b \u0936\u0942\u0928\u094d\u092f \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0915\u0930\u0928\u093e \u0939\u094b\u0917\u093e\u0964 \u092f\u0926\u093f \u0938\u092e\u093e\u0927\u093e\u0928 \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0902, \u0924\u094b \u0935\u0947 x-\u0905\u0915\u094d\u0937 \u0915\u0947 \u0915\u091f\u093e\u0935 \u0939\u094b\u0902\u0917\u0947\u0964<\/p>\n<p>   <a name=\"3\"><\/a><\/p>\n<h2>\u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947 \u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=393s\" target=\"_blank\" rel=\"noopener\"><strong>\u091c\u092c \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923<\/strong><\/a> \u092e\u093e\u0928\u0915 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u094b \u0906\u092a\u0915\u0947 \u092a\u093e\u0938 \u0926\u094b \u0935\u093f\u0915\u0932\u094d\u092a \u0939\u094b\u0924\u0947 \u0939\u0948\u0902: 1) \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 \u092c\u0926\u0932\u0947\u0902 \u092f\u093e 2) \u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0914\u0930 x-\u0905\u0915\u094d\u0937 \u0915\u0947 \u0915\u091f\u093e\u0935 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0964 \u0926\u094b\u0928\u094b\u0902 \u0935\u093f\u0927\u093f\u092f\u094b\u0902 \u0915\u0940 \u0905\u092a\u0928\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901 \u0939\u0948\u0902\u0964 \u0926\u0942\u0938\u0930\u093e \u0906\u092e \u0924\u094c\u0930 \u092a\u0930 \u0924\u0947\u091c\u093c \u0939\u094b\u0924\u093e \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u092a\u0930\u0935\u0932\u092f \u0939\u092e\u0947\u0936\u093e x-\u0905\u0915\u094d\u0937 \u0915\u094b \u0928\u0939\u0940\u0902 \u0915\u093e\u091f\u0924\u093e, \u092a\u0939\u0932\u093e \u0905\u0927\u093f\u0915 \u091c\u091f\u093f\u0932 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u091c\u0948\u0938\u093e \u0915\u093f \u0939\u092e \u092c\u093e\u0926 \u092e\u0947\u0902 \u0926\u0947\u0916\u0947\u0902\u0917\u0947, \u0907\u0938\u0947 \u0938\u094d\u0935\u091a\u093e\u0932\u093f\u0924 \u0915\u0930\u0928\u093e \u0938\u0930\u0932 \u0939\u0948\u0964 \u0939\u092e \u0926\u094b\u0928\u094b\u0902 \u0935\u093f\u0915\u0932\u094d\u092a\u094b\u0902 \u0915\u0940 \u091c\u093e\u0902\u091a \u0915\u0930\u0947\u0902\u0917\u0947 \u0924\u093e\u0915\u093f \u0906\u092a \u0905\u092a\u0928\u0940 \u092a\u094d\u0930\u093e\u0925\u092e\u093f\u0915\u0924\u093e\u0913\u0902 \u0914\u0930 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e\u0913\u0902 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0928\u093f\u0930\u094d\u0923\u092f \u0932\u0947 \u0938\u0915\u0947\u0902\u0964<\/p>\n<h3>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924 \u0915\u0930\u0928\u093e<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=475s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928<\/strong><\/a> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u094d\u0915 \u0926\u094d\u0935\u093e\u0930\u093e \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u0939\u093e\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">a,b,c\\in\\mathbb{R}<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">a \\neq 0.<\/span>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td width=\"50\">(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y = ax^2 + bx + c<\/span><\/td>\n<td>; \u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y = a\\left[x^2 + \\dfrac{b}{a}x + \\dfrac{c}{a}\\right]<\/span><\/td>\n<td>; <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0938\u0947 \u0915\u093e\u0930\u0915 \u092c\u0928\u093e\u0928\u093e<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y = a\\left[\\left(x + \\dfrac{b}{2a}\\right)^2 - \\dfrac{b^2}{4a^2} + \\dfrac{c}{a}\\right]<\/span><\/td>\n<td>; \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\left(x + \\dfrac{b}{2a}\\right)^2 = x^2 + \\dfrac{b}{a}x + \\dfrac{b^2}{4a^2}<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y = a\\left[\\left(x + \\dfrac{b}{2a}\\right)^2 + \\dfrac{4ac - b^2}{4a^2}\\right]<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y = a\\left(x + \\dfrac{b}{2a}\\right)^2 + \\dfrac{4ac - b^2}{4a}<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y = a\\left(x + \\dfrac{b}{2a}\\right)^2 + \\left(c - \\dfrac{b^2}{4a}\\right)<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\left[x - \\left(- \\dfrac{b}{2a}\\right)\\right]^2 = \\dfrac{1}{a}\\left[y - \\left(c - \\dfrac{b^2}{4a}\\right)\\right]<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\left[x - \\left(- \\dfrac{b}{2a}\\right)\\right]^2 = 4\\left(\\dfrac{1}{4a}\\right)\\left[y - \\left(c - \\dfrac{b^2}{4a}\\right)\\right]<\/span><\/td>\n<td>; \u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u0938\u092e\u0940\u0915\u0930\u0923<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0907\u0938\u0938\u0947 \u0939\u092e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947 \u092e\u093f\u0932\u0940 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u094b \u092e\u093e\u0928\u0915 \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u0947 \u0938\u093e\u0925 \u091c\u094b\u0921\u093c\u0915\u0930 \u0938\u092d\u0940 \u0906\u0935\u0936\u094d\u092f\u0915 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0928\u093f\u0915\u093e\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<ul style=\"text-align: justify;\">\n<li><strong>\u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938:<\/strong> \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0) = \\left(-\\dfrac{b}{2a}, c - \\dfrac{b^2}{4a}\\right)<\/span><\/li>\n<li><strong>\u092b\u094b\u0915\u0938 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f:<\/strong> \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938 \u0938\u0947 \u090a\u092a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">f = \\dfrac{1}{4a}<\/span> \u0907\u0915\u093e\u0907\u092f\u094b\u0902 \u092a\u0930<\/li>\n<li><strong>\u092b\u094b\u0915\u0938:<\/strong> \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">(x_0,y_0 + f) = \\left(-\\dfrac{b}{2a}, c - \\dfrac{b^2}{4a} + \\dfrac{1}{4a}\\right)<\/span><\/li>\n<li><strong>\u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0930\u0947\u0916\u093e:<\/strong> \u0938\u092e\u0940\u0915\u0930\u0923 <span class=\"katex-eq\" data-katex-display=\"false\">y = y_0 - f = c - \\dfrac{b^2}{4a} - \\dfrac{1}{4a}<\/span><\/li>\n<li><strong>\u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0927\u0941\u0930\u0940:<\/strong> \u0938\u092e\u0940\u0915\u0930\u0923 <span class=\"katex-eq\" data-katex-display=\"false\">x = x_0 = - \\dfrac{b}{2a}<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u0914\u0930 \u092f\u0939\u093e\u0902 \u0938\u0947, \u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0909\u0938\u0940 \u0924\u0930\u0939 \u0938\u0947 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u091c\u0948\u0938\u093e \u0939\u092e\u0928\u0947 \u092a\u0939\u0932\u0947 \u0926\u0947\u0916\u093e \u0925\u093e\u0964<\/p>\n<h3>\u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0914\u0930 x-\u0905\u0915\u094d\u0937 \u0915\u0947 \u0915\u091f\u093e\u0935 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=769s\" target=\"_blank\" rel=\"noopener\"><strong>\u091c\u092c \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u092a\u0930\u0935\u0932\u092f \u0915\u093e \u0938\u092e\u0940\u0915\u0930\u0923<\/strong><\/a> \u092e\u093e\u0928\u0915 \u0930\u0942\u092a <span class=\"katex-eq\" data-katex-display=\"false\">y = ax^2 + bx + c<\/span> \u092e\u0947\u0902 \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b x-\u0905\u0915\u094d\u0937 \u0915\u0947 \u0915\u091f\u093e\u0935 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u093e \u0905\u092a\u0947\u0915\u094d\u0937\u093e\u0915\u0943\u0924 \u0938\u0930\u0932 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u0938 \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u0932 \u0915\u0930\u0947\u0902<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">ax^2 + bx + c = 0<\/span>\n<p style=\"text-align: justify;\">\u091c\u092c \u0910\u0938\u093e \u0915\u0930\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u094b, \u0939\u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">x_2<\/span> \u0915\u091f\u093e\u0935 \u092e\u093f\u0932\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1 = \\dfrac{-b + \\sqrt{b^2 - 4ac}}{2a}<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x_2 = \\dfrac{-b - \\sqrt{b^2 - 4ac}}{2a}<\/span>\n<p style=\"text-align: justify;\">\u091a\u0942\u0902\u0915\u093f \u092a\u0930\u0935\u0932\u092f \u0938\u092e\u0930\u0942\u092a \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0927\u0941\u0930\u0940 \u0915\u0940 \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u094b\u0917\u0940:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x = x_0 = \\dfrac{x_1 + x_2}{2} = -\\dfrac{b}{2a}<\/span>\n<p style=\"text-align: justify;\">\u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0927\u0941\u0930\u0940 \u0905\u0928\u093f\u0935\u093e\u0930\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u092a\u0930\u0935\u0932\u092f \u0915\u0947 \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938 \u0938\u0947 \u0939\u094b\u0915\u0930 \u0917\u0941\u091c\u0930\u0924\u0940 \u0939\u0948, \u091c\u093f\u0938\u0915\u0947 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0939\u094b\u0902\u0917\u0947:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_0, y_0) = \\left( -\\dfrac{b}{2a}, y(x_0) \\right)<\/span>\n<p style=\"text-align: justify;\">\u091c\u0939\u093e\u0902<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y_0 = y\\left(-\\dfrac{b}{2a}\\right) = a\\left(-\\dfrac{b}{2a}\\right)^2 + b\\left(-\\dfrac{b}{2a}\\right) + c = c - \\dfrac{b^2}{4a}<\/span>\n<p style=\"text-align: justify;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0939\u092e \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938 \u0915\u0947 \u0909\u0928 \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915\u094b\u0902 \u092a\u0930 \u092a\u0939\u0941\u0902\u091a\u0924\u0947 \u0939\u0948\u0902 \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0939\u092e\u0928\u0947 \u0905\u0928\u094d\u092f \u0924\u0930\u0940\u0915\u094b\u0902 \u0938\u0947 \u092d\u0940 \u092a\u0939\u0932\u0947 \u0939\u0940 \u091c\u093e\u0928 \u0932\u093f\u092f\u093e \u0925\u093e:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_0, y_0) = \\left( -\\dfrac{b}{2a}, c - \\dfrac{b^2}{4a} \\right)<\/span>\n<p style=\"text-align: justify;\">\u092b\u094b\u0915\u0938 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f, \u091c\u0948\u0938\u093e \u0915\u093f \u0939\u092e\u0928\u0947 \u0926\u0947\u0916\u093e, <span class=\"katex-eq\" data-katex-display=\"false\">f = \\dfrac{1}{4a}<\/span> \u0939\u0948, \u0914\u0930 \u0907\u0938\u0938\u0947 \u0939\u092e \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0930\u0947\u0916\u093e, \u092b\u094b\u0915\u0938, \u0914\u0930 \u0938\u092d\u0940 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u0939\u092e\u0947\u0902 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947 \u092e\u093f\u0932\u0940 \u0925\u0940\u0964<\/p>\n<p>   <a name=\"4\"><\/a><\/p>\n<h2>Excel \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u094d\u0935\u091a\u093e\u0932\u093f\u0924 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=C6DbrJDiZTM&amp;t=1086s\" target=\"_blank\" rel=\"noopener\"><strong>\u0907\u0928 \u0938\u092d\u0940 \u0924\u0930\u094d\u0915\u094b\u0902 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926<\/strong><\/a>, \u0905\u092c \u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u0930\u0935\u0932\u092f \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e \u0915\u094b \u0938\u094d\u0935\u091a\u093e\u0932\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 Excel \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0915\u0930\u0928\u093e \u092c\u0939\u0941\u0924 \u0906\u0938\u093e\u0928 \u0939\u0948\u0964 \u0906\u092a \u090f\u0915 \u0909\u0926\u093e\u0939\u0930\u0923 <a href=\"https:\/\/drive.google.com\/file\/d\/1LbNOKHHfzlPgHI3_NSzuB_6_b7KmXlTd\/view?usp=sharing\" rel=\"noopener\" target=\"_blank\">\u092f\u0939\u093e\u0902<\/a> \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u092a\u0930\u0935\u0932\u092f \u0914\u0930 \u0909\u0928\u0915\u0947 \u0917\u094d\u0930\u093e\u092b\u093c \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901 \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u0913\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u0909\u0928\u0915\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0938\u092e\u0940\u0915\u0930\u0923 \u0914\u0930 \u092e\u093e\u0928\u0915 \u0930\u0942\u092a \u0938\u0947, \u092f\u0939 \u0938\u092e\u091d\u093e\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u0915\u0948\u0938\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0924\u0924\u094d\u0935\u094b\u0902 \u091c\u0948\u0938\u0947 \u0935\u0930\u094d\u091f\u0947\u0915\u094d\u0938, \u092b\u094b\u0915\u0938, \u0928\u093f\u0930\u094d\u0926\u0947\u0936\u093e\u0902\u0915 \u0930\u0947\u0916\u093e, \u0938\u092e\u0930\u0942\u092a\u0924\u093e \u0927\u0941\u0930\u0940, \u0914\u0930 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 x-\u0905\u0915\u094d\u0937 \u0915\u0947 \u0915\u091f\u093e\u0935\u094b\u0902 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0940 \u091c\u093e\u090f\u0964 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28929,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":2,"footnotes":""},"categories":[577,593],"tags":[],"class_list":["post-28937","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-577","category-593"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ 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\u092a\u0930\u0935\u0932\u092f\u094b\u0902 \u0915\u094b \u0935\u093f\u0936\u0947\u0937\u0924\u093e \u0915\u0930\u0928\u093e \u0938\u0940\u0916\u0947\u0902\u0964\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/hi\/\u092a\u0930\u0935\u0932\u092f-\u0914\u0930-\u0909\u0928\u0915\u0947-\u0917\u094d\u0930\u093e\u092b\u093c-\u0915\u0940-\u0935\u093f\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-04-27T13:00:19+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-22T02:16:05+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/focodirectriz-1024x467.png\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta 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