{"id":2534,"date":"2025-06-04T04:48:09","date_gmt":"2025-06-04T04:48:09","guid":{"rendered":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/2025\/06\/04\/0411-tung-do-goc-la-gi-cach-xac-dinh-va-ung-dung-trong-toan-hoc\/"},"modified":"2025-06-04T04:48:09","modified_gmt":"2025-06-04T04:48:09","slug":"0411-tung-do-goc-la-gi-cach-xac-dinh-va-ung-dung-trong-toan-hoc","status":"publish","type":"post","link":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/2025\/06\/04\/0411-tung-do-goc-la-gi-cach-xac-dinh-va-ung-dung-trong-toan-hoc\/","title":{"rendered":"Tung \u0110\u1ed9 G\u1ed1c L\u00e0 G\u00ec? C\u00e1ch X\u00e1c \u0110\u1ecbnh V\u00e0 \u1ee8ng D\u1ee5ng Trong To\u00e1n H\u1ecdc"},"content":{"rendered":"

B\u1ea1n \u0111ang g\u1eb7p kh\u00f3 kh\u0103n trong vi\u1ec7c hi\u1ec3u kh\u00e1i ni\u1ec7m <\/span>Tung \u0111\u1ed9 G\u1ed1c<\/a>? CAUHOI2025.EDU.VN s\u1ebd gi\u00fap b\u1ea1n kh\u00e1m ph\u00e1 m\u1ecdi kh\u00eda c\u1ea1nh c\u1ee7a tung \u0111\u1ed9 g\u1ed1c, t\u1eeb \u0111\u1ecbnh ngh\u0129a c\u01a1 b\u1ea3n, c\u00e1ch x\u00e1c \u0111\u1ecbnh, \u0111\u1ebfn c\u00e1c \u1ee9ng d\u1ee5ng quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 \u0111\u1eddi s\u1ed1ng. Ch\u00fang t\u00f4i s\u1ebd cung c\u1ea5p nh\u1eefng ki\u1ebfn th\u1ee9c d\u1ec5 hi\u1ec3u, v\u00ed d\u1ee5 minh h\u1ecda c\u1ee5 th\u1ec3 v\u00e0 c\u00e1c b\u00e0i t\u1eadp th\u1ef1c h\u00e0nh \u0111\u1ec3 b\u1ea1n n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c n\u00e0y.<\/span><\/p>\n

Tung \u0111\u1ed9 g\u1ed1c kh\u00f4ng ch\u1ec9 l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc kh\u00f4 khan m\u00e0 c\u00f2n l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 h\u1eefu \u00edch \u0111\u1ec3 gi\u1ea3i quy\u1ebft nhi\u1ec1u v\u1ea5n \u0111\u1ec1 th\u1ef1c t\u1ebf. H\u00e3y c\u00f9ng CAUHOI2025.EDU.VN kh\u00e1m ph\u00e1 nh\u1eefng \u0111i\u1ec1u th\u00fa v\u1ecb v\u1ec1 tung \u0111\u1ed9 g\u1ed1c nh\u00e9!<\/span><\/p>\n

1. Tung \u0110\u1ed9 G\u1ed1c L\u00e0 G\u00ec? \u0110\u1ecbnh Ngh\u0129a Chi Ti\u1ebft<\/span><\/h2>\n

Tung \u0111\u1ed9 g\u1ed1c, c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u201cintercept\u201d trong ti\u1ebfng Anh, l\u00e0 \u0111i\u1ec3m m\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng ho\u1eb7c \u0111\u01b0\u1eddng cong c\u1eaft tr\u1ee5c tung (tr\u1ee5c y) trong h\u1ec7 t\u1ecda \u0111\u1ed9 Descartes. N\u00f3i m\u1ed9t c\u00e1ch \u0111\u01a1n gi\u1ea3n, tung \u0111\u1ed9 g\u1ed1c l\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a y khi x b\u1eb1ng 0.<\/span><\/p>\n

1.1. Gi\u1ea3i th\u00edch c\u1eb7n k\u1ebd v\u1ec1 tung \u0111\u1ed9 g\u1ed1c<\/span><\/h3>\n

Trong ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng y = ax + b, tung \u0111\u1ed9 g\u1ed1c ch\u00ednh l\u00e0 h\u1ec7 s\u1ed1 b. \u0110i\u1ec3m (0, b) l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u1edbi tr\u1ee5c tung.<\/span><\/p>\n

V\u00ed d\u1ee5:<\/span><\/p>\n

    \n
  1. <\/span>Trong ph\u01b0\u01a1ng tr\u00ecnh y = 2x + 3, tung \u0111\u1ed9 g\u1ed1c l\u00e0 3.<\/span><\/li>\n
  2. <\/span>Trong ph\u01b0\u01a1ng tr\u00ecnh y = -x \u2013 5, tung \u0111\u1ed9 g\u1ed1c l\u00e0 -5.<\/span><\/li>\n<\/ol>\n

    1.2. Ph\u00e2n bi\u1ec7t tung \u0111\u1ed9 g\u1ed1c v\u00e0 ho\u00e0nh \u0111\u1ed9 g\u1ed1c<\/span><\/h3>\n

    \u0110\u1ec3 tr\u00e1nh nh\u1ea7m l\u1eabn, b\u1ea1n c\u1ea7n ph\u00e2n bi\u1ec7t r\u00f5 r\u00e0ng tung \u0111\u1ed9 g\u1ed1c v\u00e0 ho\u00e0nh \u0111\u1ed9 g\u1ed1c:<\/span><\/p>\n

      \n
    1. <\/span>Tung \u0111\u1ed9 g\u1ed1c:<\/strong> Giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u1edbi tr\u1ee5c tung (tr\u1ee5c y).<\/span><\/li>\n
    2. <\/span>Ho\u00e0nh \u0111\u1ed9 g\u1ed1c:<\/strong> Giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u1edbi tr\u1ee5c ho\u00e0nh (tr\u1ee5c x).<\/span><\/li>\n<\/ol>\n

      1.3. \u00dd ngh\u0129a h\u00ecnh h\u1ecdc c\u1ee7a tung \u0111\u1ed9 g\u1ed1c<\/span><\/h3>\n

      Tung \u0111\u1ed9 g\u1ed1c cho bi\u1ebft v\u1ecb tr\u00ed ban \u0111\u1ea7u c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng tr\u00ean tr\u1ee5c tung. N\u00f3 gi\u00fap ch\u00fang ta h\u00ecnh dung \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y n\u1eb1m \u1edf \u0111\u00e2u trong h\u1ec7 t\u1ecda \u0111\u1ed9.<\/span><\/p>\n

      2. C\u00e1ch X\u00e1c \u0110\u1ecbnh Tung \u0110\u1ed9 G\u1ed1c C\u1ee7a M\u1ed9t \u0110\u01b0\u1eddng Th\u1eb3ng<\/span><\/h2>\n

      C\u00f3 nhi\u1ec1u c\u00e1ch \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh tung \u0111\u1ed9 g\u1ed1c c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng, t\u00f9y thu\u1ed9c v\u00e0o th\u00f4ng tin b\u1ea1n c\u00f3:<\/span><\/p>\n

      2.1. T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng<\/span><\/h3>\n

      N\u1ebfu b\u1ea1n c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng d\u1ea1ng y = ax + b, tung \u0111\u1ed9 g\u1ed1c ch\u00ednh l\u00e0 h\u1ec7 s\u1ed1 b.<\/span><\/p>\n

      V\u00ed d\u1ee5:<\/span><\/p>\n

        \n
      1. <\/span>Cho ph\u01b0\u01a1ng tr\u00ecnh y = 5x \u2013 2, tung \u0111\u1ed9 g\u1ed1c l\u00e0 -2.<\/span><\/li>\n
      2. <\/span>Cho ph\u01b0\u01a1ng tr\u00ecnh y = -3x + 7, tung \u0111\u1ed9 g\u1ed1c l\u00e0 7.<\/span><\/li>\n<\/ol>\n

        2.2. Khi bi\u1ebft h\u1ec7 s\u1ed1 g\u00f3c v\u00e0 m\u1ed9t \u0111i\u1ec3m thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng<\/span><\/h3>\n

        N\u1ebfu b\u1ea1n bi\u1ebft h\u1ec7 s\u1ed1 g\u00f3c (a) v\u00e0 t\u1ecda \u0111\u1ed9 m\u1ed9t \u0111i\u1ec3m (x\u2081, y\u2081) thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng, b\u1ea1n c\u00f3 th\u1ec3 t\u00ecm tung \u0111\u1ed9 g\u1ed1c (b) b\u1eb1ng c\u00e1ch thay c\u00e1c gi\u00e1 tr\u1ecb n\u00e0y v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh y = ax + b v\u00e0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 t\u00ecm b.<\/span><\/p>\n

        V\u00ed d\u1ee5:<\/span><\/p>\n

        \u0110\u01b0\u1eddng th\u1eb3ng c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c l\u00e0 2 v\u00e0 \u0111i qua \u0111i\u1ec3m (1, 5). T\u00ecm tung \u0111\u1ed9 g\u1ed1c.<\/span><\/p>\n

        Gi\u1ea3i:<\/span><\/p>\n

        Thay x = 1, y = 5, a = 2 v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh y = ax + b, ta c\u00f3:<\/span><\/p>\n

        5 = 2 * 1 + b<\/span><\/p>\n

        => b = 3<\/span><\/p>\n

        V\u1eady tung \u0111\u1ed9 g\u1ed1c l\u00e0 3.<\/span><\/p>\n

        2.3. Khi bi\u1ebft t\u1ecda \u0111\u1ed9 hai \u0111i\u1ec3m thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng<\/span><\/h3>\n

        N\u1ebfu b\u1ea1n bi\u1ebft t\u1ecda \u0111\u1ed9 hai \u0111i\u1ec3m (x\u2081, y\u2081) v\u00e0 (x\u2082, y\u2082) thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng, b\u1ea1n c\u00f3 th\u1ec3 t\u00ecm tung \u0111\u1ed9 g\u1ed1c b\u1eb1ng c\u00e1ch:<\/span><\/p>\n

          \n
        1. <\/span>T\u00ednh h\u1ec7 s\u1ed1 g\u00f3c (a) b\u1eb1ng c\u00f4ng th\u1ee9c: a = (y\u2082 \u2013 y\u2081) \/ (x\u2082 \u2013 x\u2081)<\/span><\/li>\n
        2. <\/span>Ch\u1ecdn m\u1ed9t trong hai \u0111i\u1ec3m v\u00e0 thay v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh y = ax + b \u0111\u1ec3 t\u00ecm b.<\/span><\/li>\n<\/ol>\n

          V\u00ed d\u1ee5:<\/span><\/p>\n

          \u0110\u01b0\u1eddng th\u1eb3ng \u0111i qua hai \u0111i\u1ec3m (1, 3) v\u00e0 (2, 5). T\u00ecm tung \u0111\u1ed9 g\u1ed1c.<\/span><\/p>\n

          Gi\u1ea3i:<\/span><\/p>\n

            \n
          1. <\/span>T\u00ednh h\u1ec7 s\u1ed1 g\u00f3c: a = (5 \u2013 3) \/ (2 \u2013 1) = 2<\/span><\/li>\n
          2. <\/span>Ch\u1ecdn \u0111i\u1ec3m (1, 3) v\u00e0 thay v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh y = ax + b:<\/span><\/li>\n<\/ol>\n

            3 = 2 * 1 + b<\/span><\/p>\n

            => b = 1<\/span><\/p>\n

            V\u1eady tung \u0111\u1ed9 g\u1ed1c l\u00e0 1.<\/span><\/p>\n

            H\u00ecnh \u1ea3nh minh h\u1ecda v\u1ecb tr\u00ed tung \u0111\u1ed9 g\u1ed1c tr\u00ean \u0111\u1ed3 th\u1ecb, v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft tr\u1ee5c tung t\u1ea1i \u0111i\u1ec3m c\u00f3 gi\u00e1 tr\u1ecb y l\u00e0 tung \u0111\u1ed9 g\u1ed1c. Alt text: \u0110\u1ed3 th\u1ecb minh h\u1ecda tung \u0111\u1ed9 g\u1ed1c l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u1edbi tr\u1ee5c tung.<\/em><\/p>\n

            2.4. T\u1eeb \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1<\/span><\/h3>\n

            N\u1ebfu b\u1ea1n c\u00f3 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1, tung \u0111\u1ed9 g\u1ed1c l\u00e0 gi\u00e1 tr\u1ecb y t\u1ea1i \u0111i\u1ec3m m\u00e0 \u0111\u1ed3 th\u1ecb c\u1eaft tr\u1ee5c y.<\/span><\/p>\n

            3. \u1ee8ng D\u1ee5ng C\u1ee7a Tung \u0110\u1ed9 G\u1ed1c Trong To\u00e1n H\u1ecdc<\/span><\/h2>\n

            Tung \u0111\u1ed9 g\u1ed1c l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng v\u00e0 c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng trong to\u00e1n h\u1ecdc:<\/span><\/p>\n

            3.1. X\u00e1c \u0111\u1ecbnh ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng<\/span><\/h3>\n

            Khi bi\u1ebft tung \u0111\u1ed9 g\u1ed1c v\u00e0 h\u1ec7 s\u1ed1 g\u00f3c, b\u1ea1n c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng.<\/span><\/p>\n

            3.2. Gi\u1ea3i b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn giao \u0111i\u1ec3m<\/span><\/h3>\n

            Tung \u0111\u1ed9 g\u1ed1c gi\u00fap b\u1ea1n t\u00ecm giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u1edbi tr\u1ee5c tung, t\u1eeb \u0111\u00f3 gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn giao \u0111i\u1ec3m.<\/span><\/p>\n

            3.3. Nghi\u00ean c\u1ee9u t\u00ednh ch\u1ea5t c\u1ee7a h\u00e0m s\u1ed1<\/span><\/h3>\n

            Tung \u0111\u1ed9 g\u1ed1c l\u00e0 m\u1ed9t trong nh\u1eefng y\u1ebfu t\u1ed1 quan tr\u1ecdng \u0111\u1ec3 nghi\u00ean c\u1ee9u t\u00ednh ch\u1ea5t c\u1ee7a h\u00e0m s\u1ed1, \u0111\u1eb7c bi\u1ec7t l\u00e0 h\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t.<\/span><\/p>\n

            3.4. \u1ee8ng d\u1ee5ng trong h\u00ecnh h\u1ecdc<\/span><\/h3>\n

            Tung \u0111\u1ed9 g\u1ed1c \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc li\u00ean quan \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 h\u1ec7 t\u1ecda \u0111\u1ed9.<\/span><\/p>\n

            V\u00ed d\u1ee5:<\/span><\/p>\n

            T\u00ecm ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua \u0111i\u1ec3m (2, 4) v\u00e0 c\u00f3 tung \u0111\u1ed9 g\u1ed1c b\u1eb1ng 1.<\/span><\/p>\n

            Gi\u1ea3i:<\/span><\/p>\n

            V\u00ec tung \u0111\u1ed9 g\u1ed1c b\u1eb1ng 1, ta c\u00f3 b = 1.<\/span><\/p>\n

            Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 d\u1ea1ng y = ax + 1.<\/span><\/p>\n

            Thay \u0111i\u1ec3m (2, 4) v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh, ta c\u00f3:<\/span><\/p>\n

            4 = a * 2 + 1<\/span><\/p>\n

            => 2a = 3<\/span><\/p>\n

            => a = 1.5<\/span><\/p>\n

            V\u1eady ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 y = 1.5x + 1.<\/span><\/p>\n

            4. \u1ee8ng D\u1ee5ng C\u1ee7a Tung \u0110\u1ed9 G\u1ed1c Trong \u0110\u1eddi S\u1ed1ng<\/span><\/h2>\n

            Kh\u00f4ng ch\u1ec9 gi\u1edbi h\u1ea1n trong to\u00e1n h\u1ecdc, tung \u0111\u1ed9 g\u1ed1c c\u00f2n c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf trong \u0111\u1eddi s\u1ed1ng:<\/span><\/p>\n

            4.1. Trong kinh t\u1ebf<\/span><\/h3>\n

            Trong kinh t\u1ebf, tung \u0111\u1ed9 g\u1ed1c c\u00f3 th\u1ec3 bi\u1ec3u th\u1ecb chi ph\u00ed c\u1ed1 \u0111\u1ecbnh c\u1ee7a m\u1ed9t doanh nghi\u1ec7p, t\u1ee9c l\u00e0 chi ph\u00ed kh\u00f4ng thay \u0111\u1ed5i theo s\u1ea3n l\u01b0\u1ee3ng.<\/span><\/p>\n

            4.2. Trong v\u1eadt l\u00fd<\/span><\/h3>\n

            Trong v\u1eadt l\u00fd, tung \u0111\u1ed9 g\u1ed1c c\u00f3 th\u1ec3 bi\u1ec3u th\u1ecb v\u1ecb tr\u00ed ban \u0111\u1ea7u c\u1ee7a m\u1ed9t v\u1eadt th\u1ec3 trong chuy\u1ec3n \u0111\u1ed9ng th\u1eb3ng \u0111\u1ec1u.<\/span><\/p>\n

            4.3. Trong khoa h\u1ecdc d\u1eef li\u1ec7u<\/span><\/h3>\n

            Trong khoa h\u1ecdc d\u1eef li\u1ec7u, tung \u0111\u1ed9 g\u1ed1c c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong c\u00e1c m\u00f4 h\u00ecnh h\u1ed3i quy \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n gi\u00e1 tr\u1ecb c\u1ee7a m\u1ed9t bi\u1ebfn ph\u1ee5 thu\u1ed9c khi c\u00e1c bi\u1ebfn \u0111\u1ed9c l\u1eadp b\u1eb1ng 0.<\/span><\/p>\n

            V\u00ed d\u1ee5:<\/span><\/p>\n

            M\u1ed9t c\u1eeda h\u00e0ng c\u00f3 chi ph\u00ed thu\u00ea m\u1eb7t b\u1eb1ng c\u1ed1 \u0111\u1ecbnh h\u00e0ng th\u00e1ng l\u00e0 10 tri\u1ec7u \u0111\u1ed3ng. Chi ph\u00ed n\u00e0y t\u01b0\u01a1ng \u1ee9ng v\u1edbi tung \u0111\u1ed9 g\u1ed1c trong bi\u1ec3u \u0111\u1ed3 bi\u1ec3u di\u1ec5n chi ph\u00ed c\u1ee7a c\u1eeda h\u00e0ng theo doanh thu.<\/span><\/p>\n

            5. B\u00e0i T\u1eadp V\u1eadn D\u1ee5ng V\u1ec1 Tung \u0110\u1ed9 G\u1ed1c<\/span><\/h2>\n

            \u0110\u1ec3 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c, b\u1ea1n h\u00e3y th\u1eed s\u1ee9c v\u1edbi c\u00e1c b\u00e0i t\u1eadp sau:<\/span><\/p>\n

              \n
            1. <\/span>T\u00ecm tung \u0111\u1ed9 g\u1ed1c c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng sau:<\/span><\/li>\n
            2. <\/span>y = 3x \u2013 5<\/span><\/li>\n
            3. <\/span>y = -2x + 1<\/span><\/li>\n
            4. <\/span>y = x + 4<\/span><\/li>\n
            5. <\/span>Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c l\u00e0 4 v\u00e0 tung \u0111\u1ed9 g\u1ed1c l\u00e0 -2.<\/span><\/li>\n
            6. <\/span>\u0110\u01b0\u1eddng th\u1eb3ng \u0111i qua \u0111i\u1ec3m (3, 7) v\u00e0 c\u00f3 tung \u0111\u1ed9 g\u1ed1c b\u1eb1ng 2. T\u00ecm h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng.<\/span><\/li>\n
            7. <\/span>T\u00ecm giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng y = 2x + 3 v\u1edbi tr\u1ee5c tung.<\/span><\/li>\n
            8. <\/span>M\u1ed9t doanh nghi\u1ec7p c\u00f3 chi ph\u00ed c\u1ed1 \u0111\u1ecbnh h\u00e0ng th\u00e1ng l\u00e0 20 tri\u1ec7u \u0111\u1ed3ng v\u00e0 chi ph\u00ed bi\u1ebfn \u0111\u1ed5i tr\u00ean m\u1ed7i s\u1ea3n ph\u1ea9m l\u00e0 50 ngh\u00ecn \u0111\u1ed3ng. Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u di\u1ec5n t\u1ed5ng chi ph\u00ed c\u1ee7a doanh nghi\u1ec7p theo s\u1ed1 l\u01b0\u1ee3ng s\u1ea3n ph\u1ea9m. T\u00ecm tung \u0111\u1ed9 g\u1ed1c v\u00e0 gi\u1ea3i th\u00edch \u00fd ngh\u0129a c\u1ee7a n\u00f3.<\/span><\/li>\n<\/ol>\n

              6. Nh\u1eefng L\u01b0u \u00dd Quan Tr\u1ecdng Khi L\u00e0m B\u00e0i T\u1eadp V\u1ec1 Tung \u0110\u1ed9 G\u1ed1c<\/span><\/h2>\n

              Khi gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp v\u1ec1 tung \u0111\u1ed9 g\u1ed1c, b\u1ea1n c\u1ea7n l\u01b0u \u00fd nh\u1eefng \u0111i\u1ec1u sau:<\/span><\/p>\n

                \n
              1. <\/span>\u0110\u1ecdc k\u1ef9 \u0111\u1ec1 b\u00e0i:<\/strong> X\u00e1c \u0111\u1ecbnh r\u00f5 y\u00eau c\u1ea7u c\u1ee7a \u0111\u1ec1 b\u00e0i v\u00e0 th\u00f4ng tin \u0111\u00e3 cho.<\/span><\/li>\n
              2. <\/span>Nh\u1edb c\u00f4ng th\u1ee9c:<\/strong> N\u1eafm v\u1eefng c\u00e1c c\u00f4ng th\u1ee9c li\u00ean quan \u0111\u1ebfn tung \u0111\u1ed9 g\u1ed1c, h\u1ec7 s\u1ed1 g\u00f3c v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng.<\/span><\/li>\n
              3. <\/span>Ki\u1ec3m tra k\u1ebft qu\u1ea3:<\/strong> Sau khi gi\u1ea3i xong, h\u00e3y ki\u1ec3m tra l\u1ea1i k\u1ebft qu\u1ea3 \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o t\u00ednh ch\u00ednh x\u00e1c.<\/span><\/li>\n
              4. <\/span>V\u1ebd h\u00ecnh minh h\u1ecda:<\/strong> N\u1ebfu c\u00f3 th\u1ec3, h\u00e3y v\u1ebd h\u00ecnh minh h\u1ecda \u0111\u1ec3 d\u1ec5 h\u00ecnh dung v\u00e0 gi\u1ea3i b\u00e0i to\u00e1n.<\/span><\/li>\n<\/ol>\n

                7. C\u00e2u H\u1ecfi Th\u01b0\u1eddng G\u1eb7p V\u1ec1 Tung \u0110\u1ed9 G\u1ed1c (FAQ)<\/span><\/h2>\n

                D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 tung \u0111\u1ed9 g\u1ed1c:<\/span><\/p>\n

                  \n
                1. <\/span>Tung \u0111\u1ed9 g\u1ed1c c\u00f3 th\u1ec3 l\u00e0 s\u1ed1 \u00e2m kh\u00f4ng?<\/strong><\/li>\n
                2. <\/span>C\u00f3, tung \u0111\u1ed9 g\u1ed1c c\u00f3 th\u1ec3 l\u00e0 s\u1ed1 \u00e2m, s\u1ed1 d\u01b0\u01a1ng ho\u1eb7c b\u1eb1ng 0.<\/span><\/li>\n
                3. <\/span>\u0110\u01b0\u1eddng th\u1eb3ng song song v\u1edbi tr\u1ee5c ho\u00e0nh c\u00f3 tung \u0111\u1ed9 g\u1ed1c kh\u00f4ng?<\/strong><\/li>\n
                4. <\/span>C\u00f3, \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi tr\u1ee5c ho\u00e0nh c\u00f3 tung \u0111\u1ed9 g\u1ed1c l\u00e0 gi\u00e1 tr\u1ecb y c\u1ee7a m\u1ecdi \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3.<\/span><\/li>\n
                5. <\/span>\u0110\u01b0\u1eddng th\u1eb3ng \u0111i qua g\u1ed1c t\u1ecda \u0111\u1ed9 c\u00f3 tung \u0111\u1ed9 g\u1ed1c b\u1eb1ng bao nhi\u00eau?<\/strong><\/li>\n
                6. <\/span>\u0110\u01b0\u1eddng th\u1eb3ng \u0111i qua g\u1ed1c t\u1ecda \u0111\u1ed9 c\u00f3 tung \u0111\u1ed9 g\u1ed1c b\u1eb1ng 0.<\/span><\/li>\n
                7. <\/span>L\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 t\u00ecm tung \u0111\u1ed9 g\u1ed1c tr\u00ean m\u00e1y t\u00ednh c\u1ea7m tay?<\/strong><\/li>\n
                8. <\/span>B\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ch\u1ee9c n\u0103ng v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a m\u00e1y t\u00ednh c\u1ea7m tay \u0111\u1ec3 t\u00ecm tung \u0111\u1ed9 g\u1ed1c b\u1eb1ng c\u00e1ch x\u00e1c \u0111\u1ecbnh giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u1edbi tr\u1ee5c tung.<\/span><\/li>\n
                9. <\/span>Tung \u0111\u1ed9 g\u1ed1c c\u00f3 \u1ee9ng d\u1ee5ng g\u00ec trong th\u1ef1c t\u1ebf ngo\u00e0i nh\u1eefng v\u00ed d\u1ee5 \u0111\u00e3 n\u00eau?<\/strong><\/li>\n
                10. <\/span>Tung \u0111\u1ed9 g\u1ed1c c\u00f2n \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng trong vi\u1ec7c thi\u1ebft k\u1ebf \u0111\u1ed3 th\u1ecb, ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u00e0 d\u1ef1 b\u00e1o xu h\u01b0\u1edbng.<\/span><\/li>\n<\/ol>\n

                  8. T\u00ecm Hi\u1ec3u Th\u00eam V\u1ec1 C\u00e1c Kh\u00e1i Ni\u1ec7m Li\u00ean Quan \u0110\u1ebfn Tung \u0110\u1ed9 G\u1ed1c T\u1ea1i CAUHOI2025.EDU.VN<\/span><\/h2>\n

                  \u0110\u1ec3 m\u1edf r\u1ed9ng ki\u1ebfn th\u1ee9c v\u00e0 hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 tung \u0111\u1ed9 g\u1ed1c, b\u1ea1n c\u00f3 th\u1ec3 t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 c\u00e1c kh\u00e1i ni\u1ec7m li\u00ean quan t\u1ea1i CAUHOI2025.EDU.VN:<\/span><\/p>\n

                    \n
                  1. <\/span>H\u1ec7 s\u1ed1 g\u00f3c:<\/strong> Kh\u00e1i ni\u1ec7m, c\u00f4ng th\u1ee9c v\u00e0 \u1ee9ng d\u1ee5ng.<\/span><\/li>\n
                  2. <\/span>Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng:<\/strong> C\u00e1c d\u1ea1ng ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 c\u00e1ch vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng.<\/span><\/li>\n
                  3. <\/span>H\u00e0m s\u1ed1 b\u1eadc nh\u1ea5t:<\/strong> \u0110\u1ecbnh ngh\u0129a, t\u00ednh ch\u1ea5t v\u00e0 \u0111\u1ed3 th\u1ecb.<\/span><\/li>\n
                  4. <\/span>H\u1ec7 t\u1ecda \u0111\u1ed9 Descartes:<\/strong> C\u1ea5u tr\u00fac, c\u00e1ch x\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m v\u00e0 \u1ee9ng d\u1ee5ng.<\/span><\/li>\n<\/ol>\n

                    CAUHOI2025.EDU.VN cung c\u1ea5p c\u00e1c b\u00e0i vi\u1ebft chi ti\u1ebft, d\u1ec5 hi\u1ec3u v\u00e0 \u0111\u01b0\u1ee3c c\u1eadp nh\u1eadt th\u01b0\u1eddng xuy\u00ean \u0111\u1ec3 gi\u00fap b\u1ea1n n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c to\u00e1n h\u1ecdc.<\/span><\/p>\n

                    H\u00ecnh \u1ea3nh minh h\u1ecda h\u1ec7 t\u1ecda \u0111\u1ed9 Descartes, ch\u00fa th\u00edch r\u00f5 tr\u1ee5c ho\u00e0nh (x) v\u00e0 tr\u1ee5c tung (y). Alt text: Minh h\u1ecda h\u1ec7 t\u1ecda \u0111\u1ed9 Descartes v\u1edbi tr\u1ee5c x v\u00e0 y.<\/em><\/p>\n

                    9. K\u1ebft Lu\u1eadn<\/span><\/h2>\n

                    Hy v\u1ecdng b\u00e0i vi\u1ebft n\u00e0y \u0111\u00e3 gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 tung \u0111\u1ed9 g\u1ed1c, c\u00e1ch x\u00e1c \u0111\u1ecbnh v\u00e0 \u1ee9ng d\u1ee5ng c\u1ee7a n\u00f3 trong to\u00e1n h\u1ecdc v\u00e0 \u0111\u1eddi s\u1ed1ng. Tung \u0111\u1ed9 g\u1ed1c l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng v\u00e0 h\u1eefu \u00edch, gi\u00fap ch\u00fang ta gi\u1ea3i quy\u1ebft nhi\u1ec1u v\u1ea5n \u0111\u1ec1 th\u1ef1c t\u1ebf.<\/span><\/p>\n

                    \u0110\u1ec3 n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c n\u00e0y, b\u1ea1n h\u00e3y l\u00e0m th\u00eam c\u00e1c b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng v\u00e0 t\u00ecm hi\u1ec3u th\u00eam c\u00e1c kh\u00e1i ni\u1ec7m li\u00ean quan t\u1ea1i CAUHOI2025.EDU.VN.<\/span><\/p>\n

                    N\u1ebfu b\u1ea1n c\u00f3 b\u1ea5t k\u1ef3 th\u1eafc m\u1eafc n\u00e0o, \u0111\u1eebng ng\u1ea7n ng\u1ea1i li\u00ean h\u1ec7 v\u1edbi ch\u00fang t\u00f4i \u0111\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i \u0111\u00e1p. CAUHOI2025.EDU.VN lu\u00f4n s\u1eb5n s\u00e0ng h\u1ed7 tr\u1ee3 b\u1ea1n tr\u00ean con \u0111\u01b0\u1eddng chinh ph\u1ee5c ki\u1ebfn th\u1ee9c!<\/span><\/p>\n

                    10. L\u1eddi K\u00eau G\u1ecdi H\u00e0nh \u0110\u1ed9ng (CTA)<\/span><\/h2>\n

                    B\u1ea1n v\u1eabn c\u00f2n nh\u1eefng c\u00e2u h\u1ecfi ch\u01b0a \u0111\u01b0\u1ee3c gi\u1ea3i \u0111\u00e1p v\u1ec1 tung \u0111\u1ed9 g\u1ed1c ho\u1eb7c c\u00e1c v\u1ea5n \u0111\u1ec1 to\u00e1n h\u1ecdc kh\u00e1c? H\u00e3y truy c\u1eadp CAUHOI2025.EDU.VN ngay h\u00f4m nay \u0111\u1ec3 kh\u00e1m ph\u00e1 kho t\u00e0ng ki\u1ebfn th\u1ee9c phong ph\u00fa v\u00e0 nh\u1eadn \u0111\u01b0\u1ee3c s\u1ef1 h\u1ed7 tr\u1ee3 t\u1eadn t\u00ecnh t\u1eeb \u0111\u1ed9i ng\u0169 chuy\u00ean gia c\u1ee7a ch\u00fang t\u00f4i. \u0110\u1eebng b\u1ecf l\u1ee1 c\u01a1 h\u1ed9i n\u00e2ng cao tr\u00ecnh \u0111\u1ed9 v\u00e0 chinh ph\u1ee5c nh\u1eefng th\u1eed th\u00e1ch m\u1edbi!<\/span><\/p>\n

                    B\u1ea1n c\u00f3 th\u1ec3 li\u00ean h\u1ec7 v\u1edbi CAUHOI2025.EDU.VN theo \u0111\u1ecba ch\u1ec9:<\/strong><\/p>\n

                    \u0110\u1ecba ch\u1ec9: 30 P. Kh\u00e2m Thi\u00ean, Th\u1ed5 Quan, \u0110\u1ed1ng \u0110a, H\u00e0 N\u1ed9i, Vi\u1ec7t Nam<\/span><\/p>\n

                    S\u1ed1 \u0111i\u1ec7n tho\u1ea1i: +84 2435162967<\/span><\/p>\n

                    Trang web: <\/span>CauHoi2025.EDU.VN<\/a><\/p>\n

                    Ch\u00fang t\u00f4i lu\u00f4n s\u1eb5n l\u00f2ng l\u1eafng nghe v\u00e0 gi\u1ea3i \u0111\u00e1p m\u1ecdi th\u1eafc m\u1eafc c\u1ee7a b\u1ea1n!<\/span><\/p>\n

                    <\/p>\n","protected":false},"excerpt":{"rendered":"

                    B\u1ea1n \u0111ang g\u1eb7p kh\u00f3 kh\u0103n trong vi\u1ec7c hi\u1ec3u kh\u00e1i ni\u1ec7m Tung \u0111\u1ed9 G\u1ed1c? CAUHOI2025.EDU.VN s\u1ebd gi\u00fap b\u1ea1n kh\u00e1m ph\u00e1 m\u1ecdi kh\u00eda c\u1ea1nh c\u1ee7a tung \u0111\u1ed9 g\u1ed1c, t\u1eeb \u0111\u1ecbnh ngh\u0129a c\u01a1 b\u1ea3n, c\u00e1ch x\u00e1c \u0111\u1ecbnh, \u0111\u1ebfn c\u00e1c \u1ee9ng d\u1ee5ng quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 \u0111\u1eddi s\u1ed1ng. Ch\u00fang t\u00f4i s\u1ebd cung c\u1ea5p nh\u1eefng ki\u1ebfn th\u1ee9c d\u1ec5 hi\u1ec3u, […]\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2534","post","type-post","status-publish","format-standard","hentry","category-khong-phan-loai"],"_links":{"self":[{"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/posts\/2534","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/comments?post=2534"}],"version-history":[{"count":0,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/posts\/2534\/revisions"}],"wp:attachment":[{"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/media?parent=2534"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/categories?post=2534"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daotaotructuyentiengtrung.edu.vn\/index.php\/wp-json\/wp\/v2\/tags?post=2534"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}