{"id":567145,"date":"2026-07-22T10:58:33","date_gmt":"2026-07-22T03:58:33","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567145"},"modified":"2026-07-22T10:58:33","modified_gmt":"2026-07-22T03:58:33","slug":"parabol","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/parabol\/","title":{"rendered":"Parabol l\u00e0 g\u00ec? \u0110\u1ec9nh, tr\u1ee5c \u0111\u1ed1i x\u1ee9ng v\u00e0 c\u00e1ch v\u1ebd \u0111\u1ed3 th\u1ecb"},"content":{"rendered":"<p>Parabol l\u00e0 d\u1ea1ng \u0111\u1ed3 th\u1ecb h\u00ecnh ch\u1eef U quen thu\u1ed9c m\u00e0 b\u1ea1n g\u1eb7p ngay t\u1eeb nh\u1eefng b\u00e0i \u0111\u1ea7u ti\u00ean v\u1ec1 h\u00e0m s\u1ed1 b\u1eadc hai \u1edf l\u1edbp 9, l\u1edbp 10. Kh\u00f4ng ch\u1ec9 l\u00e0 ki\u1ebfn th\u1ee9c thi c\u1eed, parabol c\u00f2n xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u hi\u1ec7n t\u01b0\u1ee3ng th\u1ef1c t\u1ebf nh\u01b0 qu\u1ef9 \u0111\u1ea1o m\u1ed9t v\u1eadt \u0111\u01b0\u1ee3c n\u00e9m l\u00ean, h\u00ecnh d\u1ea1ng g\u01b0\u01a1ng c\u1ea7u hay \u0103ng-ten thu s\u00f3ng. N\u1ebfu b\u1ea1n \u0111ang ph\u00e2n v\u00e2n v\u1ec1 c\u00f4ng th\u1ee9c t\u00ednh \u0111\u1ec9nh, c\u00e1ch x\u00e1c \u0111\u1ecbnh tr\u1ee5c \u0111\u1ed1i x\u1ee9ng hay ch\u01b0a r\u00f5 c\u00e1c b\u01b0\u1edbc v\u1ebd \u0111\u1ed3 th\u1ecb sao cho ch\u00ednh x\u00e1c, nh\u1eefng ph\u1ea7n d\u01b0\u1edbi \u0111\u00e2y s\u1ebd gi\u00fap b\u1ea1n h\u1ec7 th\u1ed1ng l\u1ea1i \u0111\u1ea7y \u0111\u1ee7 \u0111\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, d\u1ec5 \u00e1p d\u1ee5ng ngay v\u00e0o b\u00e0i t\u1eadp.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-568871 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-1.jpg\" alt=\"Parabol-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>Parabol l\u00e0 g\u00ec?<\/h2>\n<p>Trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n ph\u1ed5 th\u00f4ng, parabol l\u00e0 t\u00ean g\u1ecdi c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 b\u1eadc hai c\u00f3 d\u1ea1ng y = ax\u00b2 + bx + c, v\u1edbi a, b, c l\u00e0 c\u00e1c h\u1eb1ng s\u1ed1 v\u00e0 \u0111i\u1ec1u ki\u1ec7n b\u1eaft bu\u1ed9c a kh\u00e1c 0. \u0110\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0y lu\u00f4n l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng cong \u0111\u1ed1i x\u1ee9ng, m\u1edf l\u00ean tr\u00ean ho\u1eb7c m\u1edf xu\u1ed1ng d\u01b0\u1edbi t\u00f9y theo d\u1ea5u c\u1ee7a h\u1ec7 s\u1ed1 a.<\/p>\n<p>\u1ede g\u00f3c \u0111\u1ed9 h\u00ecnh h\u1ecdc, parabol c\u00f2n \u0111\u01b0\u1ee3c xem l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng conic: t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m c\u00e1ch \u0111\u1ec1u m\u1ed9t ti\u00eau \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh v\u00e0 m\u1ed9t \u0111\u01b0\u1eddng chu\u1ea9n c\u1ed1 \u0111\u1ecbnh, c\u00f9ng nh\u00f3m v\u1edbi <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-tron-la-gi\/\">\u0111\u01b0\u1eddng tr\u00f2n<\/a> v\u00e0 c\u00e1c \u0111\u01b0\u1eddng conic kh\u00e1c. \u1ede m\u1ee9c ph\u1ed5 th\u00f4ng, b\u1ea1n ch\u1ec9 c\u1ea7n n\u1eafm ch\u1eafc d\u1ea1ng y = ax\u00b2 + bx + c l\u00e0 \u0111\u1ee7 \u0111\u1ec3 gi\u1ea3i h\u1ea7u h\u1ebft c\u00e1c d\u1ea1ng b\u00e0i.<\/p>\n<h2>T\u1ecda \u0111\u1ed9 \u0111\u1ec9nh v\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng c\u1ee7a parabol<\/h2>\n<p>\u0110\u1ec9nh v\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng l\u00e0 hai y\u1ebfu t\u1ed1 quan tr\u1ecdng nh\u1ea5t \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh v\u1ecb tr\u00ed, h\u00ecnh d\u00e1ng c\u1ee7a parabol. V\u1edbi y = ax\u00b2 + bx + c (a kh\u00e1c 0), g\u1ecdi \u0394 = b\u00b2 &#8211; 4ac, ta c\u00f3 b\u1ea3ng c\u00f4ng th\u1ee9c sau:<\/p>\n<table>\n<thead>\n<tr>\n<th>Y\u1ebfu t\u1ed1<\/th>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Bi\u1ec7t th\u1ee9c<\/td>\n<td>\u0394 = b\u00b2 &#8211; 4ac<\/td>\n<\/tr>\n<tr>\n<td>Ho\u00e0nh \u0111\u1ed9 \u0111\u1ec9nh<\/td>\n<td>x = -b\/2a<\/td>\n<\/tr>\n<tr>\n<td>Tung \u0111\u1ed9 \u0111\u1ec9nh<\/td>\n<td>y = -\u0394\/4a<\/td>\n<\/tr>\n<tr>\n<td>T\u1ecda \u0111\u1ed9 \u0111\u1ec9nh<\/td>\n<td>I(-b\/2a ; -\u0394\/4a)<\/td>\n<\/tr>\n<tr>\n<td>Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng<\/td>\n<td>\u0111\u01b0\u1eddng th\u1eb3ng x = -b\/2a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng chia parabol th\u00e0nh hai nh\u00e1nh \u0111\u1ed1i x\u1ee9ng nhau. Khi v\u1ebd \u0111\u1ed3 th\u1ecb, b\u1ea1n ch\u1ec9 c\u1ea7n kh\u1ea3o s\u00e1t k\u1ef9 m\u1ed9t nh\u00e1nh r\u1ed3i l\u1ea5y \u0111\u1ed1i x\u1ee9ng qua tr\u1ee5c \u0111\u1ec3 c\u00f3 nh\u00e1nh c\u00f2n l\u1ea1i.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-568872 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-2.jpg\" alt=\"Parabol-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>B\u1ec1 l\u00f5m c\u1ee7a parabol ph\u1ee5 thu\u1ed9c v\u00e0o d\u1ea5u h\u1ec7 s\u1ed1 a<\/h2>\n<p>D\u1ea5u c\u1ee7a h\u1ec7 s\u1ed1 a quy\u1ebft \u0111\u1ecbnh parabol &#8220;m\u1edf&#8221; l\u00ean tr\u00ean hay &#8220;\u00fap&#8221; xu\u1ed1ng d\u01b0\u1edbi, \u0111\u1ed3ng th\u1eddi cho bi\u1ebft \u0111\u1ec9nh l\u00e0 \u0111i\u1ec3m cao nh\u1ea5t hay th\u1ea5p nh\u1ea5t c\u1ee7a \u0111\u1ed3 th\u1ecb.<\/p>\n<ul>\n<li>a &gt; 0: parabol quay b\u1ec1 l\u00f5m l\u00ean tr\u00ean (d\u1ea1ng ch\u1eef U), \u0111\u1ec9nh I l\u00e0 \u0111i\u1ec3m th\u1ea5p nh\u1ea5t, h\u00e0m s\u1ed1 \u0111\u1ea1t gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t t\u1ea1i x = -b\/2a.<\/li>\n<li>a &lt; 0: parabol quay b\u1ec1 l\u00f5m xu\u1ed1ng d\u01b0\u1edbi (d\u1ea1ng ch\u1eef U ng\u01b0\u1ee3c), \u0111\u1ec9nh I l\u00e0 \u0111i\u1ec3m cao nh\u1ea5t, h\u00e0m s\u1ed1 \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t t\u1ea1i x = -b\/2a.<\/li>\n<\/ul>\n<p>M\u1eb9o nh\u1ecf \u0111\u1ec3 kh\u00f4ng nh\u1ea7m chi\u1ec1u b\u1ec1 l\u00f5m: &#8220;a d\u01b0\u01a1ng th\u00ec c\u01b0\u1eddi, a \u00e2m th\u00ec kh\u00f3c&#8221; \u2014 n\u00e9t c\u01b0\u1eddi l\u00e0 \u0111\u01b0\u1eddng cong m\u1edf l\u00ean, n\u00e9t kh\u00f3c l\u00e0 \u0111\u01b0\u1eddng cong \u00fap xu\u1ed1ng.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-568873 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-3.jpg\" alt=\"Parabol-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1c b\u01b0\u1edbc v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 parabol<\/h2>\n<p>\u0110\u1ec3 v\u1ebd ch\u00ednh x\u00e1c \u0111\u1ed3 th\u1ecb m\u1ed9t parabol, b\u1ea1n c\u00f3 th\u1ec3 l\u00e0m theo tr\u00ecnh t\u1ef1 5 b\u01b0\u1edbc sau:<\/p>\n<ol>\n<li>X\u00e1c \u0111\u1ecbnh t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh I(-b\/2a ; -\u0394\/4a).<\/li>\n<li>X\u00e1c \u0111\u1ecbnh tr\u1ee5c \u0111\u1ed1i x\u1ee9ng x = -b\/2a v\u00e0 h\u01b0\u1edbng b\u1ec1 l\u00f5m theo d\u1ea5u c\u1ee7a a.<\/li>\n<li>T\u00ecm giao \u0111i\u1ec3m v\u1edbi tr\u1ee5c tung: cho x = 0, \u0111\u01b0\u1ee3c \u0111i\u1ec3m (0; c).<\/li>\n<li>T\u00ecm giao \u0111i\u1ec3m v\u1edbi tr\u1ee5c ho\u00e0nh (n\u1ebfu c\u00f3) b\u1eb1ng c\u00e1ch gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh ax\u00b2 + bx + c = 0.<\/li>\n<li>L\u1ea5y th\u00eam 1-2 \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng qua tr\u1ee5c \u0111\u1ec3 \u0111\u1ed3 th\u1ecb m\u01b0\u1ee3t h\u01a1n, sau \u0111\u00f3 n\u1ed1i c\u00e1c \u0111i\u1ec3m b\u1eb1ng m\u1ed9t \u0111\u01b0\u1eddng cong, kh\u00f4ng n\u1ed1i b\u1eb1ng \u0111o\u1ea1n th\u1eb3ng.<\/li>\n<\/ol>\n<p>Ri\u00eang d\u1ea1ng b\u00e0i t\u00ecm giao \u0111i\u1ec3m gi\u1eefa parabol v\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng b\u1ea5t k\u1ef3, b\u1ea1n c\u1ea7n gi\u1ea3i th\u00eam m\u1ed9t <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/he-phuong-trinh\/\">h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/a> g\u1ed3m ph\u01b0\u01a1ng tr\u00ecnh parabol v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568874 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-4.jpg\" alt=\"Parabol-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>V\u00ed d\u1ee5 minh h\u1ecda c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft<\/h2>\n<h3>V\u00ed d\u1ee5 1: Parabol y = x\u00b2 &#8211; 4x + 3<\/h3>\n<p>Cho h\u00e0m s\u1ed1 y = x\u00b2 &#8211; 4x + 3 (a = 1, b = -4, c = 3). \u0394 = 16 &#8211; 12 = 4. Ho\u00e0nh \u0111\u1ed9 \u0111\u1ec9nh x = -b\/2a = 4\/2 = 2. Tung \u0111\u1ed9 \u0111\u1ec9nh y = -\u0394\/4a = -4\/4 = -1. \u0110\u1ec9nh I(2; -1), tr\u1ee5c \u0111\u1ed1i x\u1ee9ng x = 2. V\u00ec a = 1 &gt; 0, parabol quay b\u1ec1 l\u00f5m l\u00ean, \u0111\u1ec9nh l\u00e0 \u0111i\u1ec3m th\u1ea5p nh\u1ea5t. Giao Oy: x = 0 cho y = 3, t\u1ee9c (0; 3). Giao Ox: gi\u1ea3i x\u00b2 &#8211; 4x + 3 = 0 \u0111\u01b0\u1ee3c x = 1, x = 3, t\u1ee9c (1; 0) v\u00e0 (3; 0). N\u1ed1i c\u00e1c \u0111i\u1ec3m th\u00e0nh \u0111\u01b0\u1eddng cong \u0111\u1ed1i x\u1ee9ng qua x = 2.<\/p>\n<h3>V\u00ed d\u1ee5 2: Parabol y = -x\u00b2 + 2x + 3<\/h3>\n<p>Cho h\u00e0m s\u1ed1 y = -x\u00b2 + 2x + 3 (a = -1, b = 2, c = 3). \u0394 = 4 + 12 = 16. Ho\u00e0nh \u0111\u1ed9 \u0111\u1ec9nh x = -2\/(2\u00d7(-1)) = 1. Tung \u0111\u1ed9 \u0111\u1ec9nh y = -16\/(4\u00d7(-1)) = 4. \u0110\u1ec9nh I(1; 4). V\u00ec a = -1 &lt; 0, parabol quay b\u1ec1 l\u00f5m xu\u1ed1ng, \u0111\u1ec9nh l\u00e0 \u0111i\u1ec3m cao nh\u1ea5t, gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t b\u1eb1ng 4. Giao Ox: -x\u00b2 + 2x + 3 = 0 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng x\u00b2 &#8211; 2x &#8211; 3 = 0, \u0111\u01b0\u1ee3c x = 3, x = -1. Giao Oy: x = 0 cho y = 3, t\u1ee9c (0; 3).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568875 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-5.jpg\" alt=\"Parabol-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h3>V\u00ed d\u1ee5 3: \u1ee8ng d\u1ee5ng parabol trong b\u00e0i to\u00e1n th\u1ef1c t\u1ebf<\/h3>\n<p>M\u1ed9t qu\u1ea3 b\u00f3ng \u0111\u01b0\u1ee3c \u0111\u00e1 l\u00ean theo qu\u1ef9 \u0111\u1ea1o h(t) = -5t\u00b2 + 20t (h: \u0111\u1ed9 cao t\u00ednh b\u1eb1ng m\u00e9t, t: th\u1eddi gian t\u00ednh b\u1eb1ng gi\u00e2y), t\u01b0\u01a1ng \u1ee9ng a = -5, b = 20, c = 0. Th\u1eddi \u0111i\u1ec3m \u0111\u1ea1t \u0111\u1ed9 cao l\u1edbn nh\u1ea5t: t = -b\/2a = 2 (gi\u00e2y). \u0110\u1ed9 cao l\u1edbn nh\u1ea5t: h = -\u0394\/4a = -400\/-20 = 20 (m\u00e9t). V\u1eady sau 2 gi\u00e2y, b\u00f3ng \u0111\u1ea1t \u0111\u1ed9 cao 20m r\u1ed3i r\u01a1i xu\u1ed1ng, ch\u1ea1m \u0111\u1ea5t \u1edf gi\u00e2y th\u1ee9 4. V\u00ed d\u1ee5 n\u00e0y cho th\u1ea5y c\u00f4ng th\u1ee9c \u0111\u1ec9nh c\u00f2n gi\u1ea3i \u0111\u01b0\u1ee3c c\u1ea3 b\u00e0i to\u00e1n t\u1ed1i \u01b0u trong th\u1ef1c t\u1ebf, kh\u00f4ng ch\u1ec9 \u0111\u1ec3 v\u1ebd \u0111\u1ed3 th\u1ecb.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568876 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-6.jpg\" alt=\"Parabol-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/Parabol-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<table>\n<thead>\n<tr>\n<th>V\u00ed d\u1ee5<\/th>\n<th>H\u1ec7 s\u1ed1 a, b, c<\/th>\n<th>\u0110\u1ec9nh I<\/th>\n<th>Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng<\/th>\n<th>B\u1ec1 l\u00f5m<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>y = x\u00b2 &#8211; 4x + 3<\/td>\n<td>a=1; b=-4; c=3<\/td>\n<td>(2; -1)<\/td>\n<td>x = 2<\/td>\n<td>L\u00ean (a &gt; 0)<\/td>\n<\/tr>\n<tr>\n<td>y = -x\u00b2 + 2x + 3<\/td>\n<td>a=-1; b=2; c=3<\/td>\n<td>(1; 4)<\/td>\n<td>x = 1<\/td>\n<td>Xu\u1ed1ng (a &lt; 0)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>B\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n<\/h2>\n<p>B\u1ea1n c\u00f3 th\u1ec3 t\u1ef1 ki\u1ec3m tra ki\u1ebfn th\u1ee9c v\u1edbi c\u00e1c b\u00e0i t\u1eadp ng\u1eafn d\u01b0\u1edbi \u0111\u00e2y tr\u01b0\u1edbc khi xem \u0111\u00e1p s\u1ed1.<\/p>\n<ol>\n<li>Cho parabol y = x\u00b2 &#8211; 2x &#8211; 3. T\u00ecm \u0111\u1ec9nh v\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng. <em>\u0110\u00e1p s\u1ed1: I(1; -4), tr\u1ee5c x = 1.<\/em><\/li>\n<li>Cho parabol y = -2x\u00b2 + 4x + 1. Parabol l\u00f5m l\u00ean hay xu\u1ed1ng? T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a y. <em>\u0110\u00e1p s\u1ed1: a &lt; 0 n\u00ean l\u00f5m xu\u1ed1ng; y l\u1edbn nh\u1ea5t = 3 t\u1ea1i x = 1.<\/em><\/li>\n<li>Cho parabol y = 2x\u00b2 &#8211; 8x + 6. T\u00ecm giao \u0111i\u1ec3m v\u1edbi tr\u1ee5c ho\u00e0nh. <em>\u0110\u00e1p s\u1ed1: x = 1 v\u00e0 x = 3, t\u1ee9c (1; 0) v\u00e0 (3; 0).<\/em><\/li>\n<\/ol>\n<h2>M\u1ed9t s\u1ed1 l\u01b0u \u00fd khi l\u00e0m b\u00e0i v\u1ec1 parabol<\/h2>\n<p>M\u1ed9t v\u00e0i l\u1ed7i ph\u1ed5 bi\u1ebfn khi\u1ebfn k\u1ebft qu\u1ea3 sai d\u00f9 c\u00e1ch l\u00e0m \u0111\u00fang h\u01b0\u1edbng:<\/p>\n<ul>\n<li>Nh\u1ea7m d\u1ea5u khi t\u00ednh \u0394 = b\u00b2 &#8211; 4ac, nh\u1ea5t l\u00e0 khi a ho\u1eb7c c \u00e2m.<\/li>\n<li>Qu\u00ean \u0111i\u1ec1u ki\u1ec7n a kh\u00e1c 0, nh\u1eadn di\u1ec7n sai m\u1ed9t h\u00e0m b\u1eadc nh\u1ea5t th\u00e0nh parabol.<\/li>\n<li>N\u1ed1i \u0111i\u1ec3m b\u1eb1ng \u0111o\u1ea1n th\u1eb3ng thay v\u00ec \u0111\u01b0\u1eddng cong khi v\u1ebd, khi\u1ebfn h\u00ecnh d\u1ea1ng b\u1ecb m\u00e9o; \u0111\u1ed3ng th\u1eddi d\u1ec5 nh\u1ea7m gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t\/nh\u1ecf nh\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 v\u1edbi nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh khi x\u00e9t d\u1ea5u b\u1eb1ng <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/bat-phuong-trinh\/\">b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh<\/a> b\u1eadc hai.<\/li>\n<\/ul>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 parabol<\/h2>\n<h3>Parabol l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o?<\/h3>\n<p>Parabol l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 b\u1eadc hai y = ax\u00b2 + bx + c, v\u1edbi a kh\u00e1c 0. N\u1ebfu a = 0, \u0111\u1ed3 th\u1ecb ch\u1ec9 c\u00f2n l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n<h3>L\u00e0m sao \u0111\u1ec3 t\u00ecm t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh c\u1ee7a parabol?<\/h3>\n<p>T\u00ednh \u0394 = b\u00b2 &#8211; 4ac r\u1ed3i \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ec9nh I(-b\/2a; -\u0394\/4a). Ho\u1eb7c t\u00ednh x = -b\/2a tr\u01b0\u1edbc, sau \u0111\u00f3 th\u1ebf v\u00e0o h\u00e0m s\u1ed1 ban \u0111\u1ea7u \u0111\u1ec3 t\u00ecm y.<\/p>\n<h3>Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng c\u1ee7a parabol l\u00e0 g\u00ec?<\/h3>\n<p>Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = -b\/2a, \u0111i qua \u0111\u1ec9nh v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi tr\u1ee5c ho\u00e0nh, chia parabol th\u00e0nh hai nh\u00e1nh \u0111\u1ed1i x\u1ee9ng nhau.<\/p>\n<h3>Khi n\u00e0o parabol quay b\u1ec1 l\u00f5m l\u00ean, khi n\u00e0o quay xu\u1ed1ng?<\/h3>\n<p>N\u1ebfu a &gt; 0, parabol quay b\u1ec1 l\u00f5m l\u00ean v\u00e0 \u0111\u1ec9nh l\u00e0 \u0111i\u1ec3m th\u1ea5p nh\u1ea5t. N\u1ebfu a &lt; 0, parabol quay b\u1ec1 l\u00f5m xu\u1ed1ng v\u00e0 \u0111\u1ec9nh l\u00e0 \u0111i\u1ec3m cao nh\u1ea5t.<\/p>\n<h3>Parabol c\u00f3 lu\u00f4n c\u1eaft tr\u1ee5c ho\u00e0nh kh\u00f4ng?<\/h3>\n<p>Kh\u00f4ng. S\u1ed1 giao \u0111i\u1ec3m ph\u1ee5 thu\u1ed9c d\u1ea5u c\u1ee7a \u0394: \u0394 &gt; 0 c\u1eaft t\u1ea1i 2 \u0111i\u1ec3m, \u0394 = 0 ti\u1ebfp x\u00fac t\u1ea1i 1 \u0111i\u1ec3m, \u0394 &lt; 0 th\u00ec kh\u00f4ng c\u1eaft tr\u1ee5c ho\u00e0nh.<\/p>\n<h3>C\u00f3 m\u1eb9o n\u00e0o \u0111\u1ec3 v\u1ebd nhanh \u0111\u1ed3 th\u1ecb parabol kh\u00f4ng?<\/h3>\n<p>X\u00e1c \u0111\u1ecbnh \u0111\u1ec9nh, tr\u1ee5c \u0111\u1ed1i x\u1ee9ng, t\u00ecm giao \u0111i\u1ec3m v\u1edbi hai tr\u1ee5c t\u1ecda \u0111\u1ed9, l\u1ea5y th\u00eam m\u1ed9t \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng qua tr\u1ee5c r\u1ed3i n\u1ed1i b\u1eb1ng \u0111\u01b0\u1eddng cong m\u01b0\u1ee3t, kh\u00f4ng n\u1ed1i b\u1eb1ng \u0111o\u1ea1n th\u1eb3ng.<\/p>\n<h3>Parabol c\u00f3 \u1ee9ng d\u1ee5ng g\u00ec trong th\u1ef1c t\u1ebf?<\/h3>\n<p>Parabol xu\u1ea5t hi\u1ec7n trong qu\u1ef9 \u0111\u1ea1o v\u1eadt b\u1ecb n\u00e9m xi\u00ean, thi\u1ebft k\u1ebf g\u01b0\u01a1ng c\u1ea7u, \u0103ng-ten parabol gi\u00fap h\u1ed9i t\u1ee5 t\u00edn hi\u1ec7u v\u1ec1 m\u1ed9t \u0111i\u1ec3m, hay h\u00ecnh d\u00e1ng d\u00e2y v\u0103ng c\u1ee7a m\u1ed9t s\u1ed1 c\u00e2y c\u1ea7u.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>Ch\u1ec9 v\u1edbi v\u00e0i c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n \u2014 t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh, tr\u1ee5c \u0111\u1ed1i x\u1ee9ng v\u00e0 d\u1ea5u c\u1ee7a h\u1ec7 s\u1ed1 a \u2014 b\u1ea1n \u0111\u00e3 c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u00fang h\u00ecnh d\u1ea1ng v\u00e0 v\u1ebd ch\u00ednh x\u00e1c \u0111\u1ed3 th\u1ecb c\u1ee7a b\u1ea5t k\u1ef3 parabol n\u00e0o. C\u00e1ch ghi nh\u1edb t\u1ed1t nh\u1ea5t l\u00e0 luy\u1ec7n t\u1eadp v\u1edbi nhi\u1ec1u b\u1ed9 s\u1ed1 a, b, c kh\u00e1c nhau r\u1ed3i t\u1ef1 v\u1ebd l\u1ea1i \u0111\u1ed3 th\u1ecb nhi\u1ec1u l\u1ea7n. Khi \u0111\u00e3 n\u1eafm ch\u1eafc ph\u1ea7n n\u00e0y, b\u1ea1n c\u00f3 th\u1ec3 h\u1ecdc ti\u1ebfp c\u00e1c d\u1ea1ng h\u00e0m s\u1ed1 li\u00ean quan \u0111\u1ec3 h\u1ec7 th\u1ed1ng h\u00f3a ki\u1ebfn th\u1ee9c \u0111\u1ea1i s\u1ed1 l\u1edbp 10.<\/p>\n<p><script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"Parabol l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 n\u00e0o?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Parabol l\u00e0 \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 b\u1eadc hai y = ax^2 + bx + c, v\u1edbi a kh\u00e1c 0. N\u1ebfu a = 0, \u0111\u1ed3 th\u1ecb ch\u1ec9 c\u00f2n l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng.\"}},\n{\"@type\":\"Question\",\"name\":\"L\u00e0m sao \u0111\u1ec3 t\u00ecm t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh c\u1ee7a parabol?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"T\u00ednh Delta = b^2 - 4ac r\u1ed3i \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ec9nh I(-b\/2a; -Delta\/4a). Ho\u1eb7c t\u00ednh x = -b\/2a tr\u01b0\u1edbc, sau \u0111\u00f3 th\u1ebf v\u00e0o h\u00e0m s\u1ed1 ban \u0111\u1ea7u \u0111\u1ec3 t\u00ecm y.\"}},\n{\"@type\":\"Question\",\"name\":\"Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng c\u1ee7a parabol l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Tr\u1ee5c \u0111\u1ed1i x\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = -b\/2a, \u0111i qua \u0111\u1ec9nh v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi tr\u1ee5c ho\u00e0nh, chia parabol th\u00e0nh hai nh\u00e1nh \u0111\u1ed1i x\u1ee9ng nhau.\"}},\n{\"@type\":\"Question\",\"name\":\"Khi n\u00e0o parabol quay b\u1ec1 l\u00f5m l\u00ean, khi n\u00e0o quay xu\u1ed1ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"N\u1ebfu a l\u1edbn h\u01a1n 0, parabol quay b\u1ec1 l\u00f5m l\u00ean v\u00e0 \u0111\u1ec9nh l\u00e0 \u0111i\u1ec3m th\u1ea5p nh\u1ea5t. N\u1ebfu a nh\u1ecf h\u01a1n 0, parabol quay b\u1ec1 l\u00f5m xu\u1ed1ng v\u00e0 \u0111\u1ec9nh l\u00e0 \u0111i\u1ec3m cao nh\u1ea5t.\"}},\n{\"@type\":\"Question\",\"name\":\"Parabol c\u00f3 lu\u00f4n c\u1eaft tr\u1ee5c ho\u00e0nh kh\u00f4ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Kh\u00f4ng. S\u1ed1 giao \u0111i\u1ec3m ph\u1ee5 thu\u1ed9c d\u1ea5u c\u1ee7a Delta: Delta d\u01b0\u01a1ng th\u00ec c\u1eaft t\u1ea1i 2 \u0111i\u1ec3m, Delta b\u1eb1ng 0 th\u00ec ti\u1ebfp x\u00fac t\u1ea1i 1 \u0111i\u1ec3m, Delta \u00e2m th\u00ec kh\u00f4ng c\u1eaft tr\u1ee5c ho\u00e0nh.\"}},\n{\"@type\":\"Question\",\"name\":\"C\u00f3 m\u1eb9o n\u00e0o \u0111\u1ec3 v\u1ebd nhanh \u0111\u1ed3 th\u1ecb parabol kh\u00f4ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"X\u00e1c \u0111\u1ecbnh \u0111\u1ec9nh, tr\u1ee5c \u0111\u1ed1i x\u1ee9ng, t\u00ecm giao \u0111i\u1ec3m v\u1edbi hai tr\u1ee5c t\u1ecda \u0111\u1ed9, l\u1ea5y th\u00eam m\u1ed9t \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng qua tr\u1ee5c r\u1ed3i n\u1ed1i b\u1eb1ng \u0111\u01b0\u1eddng cong m\u01b0\u1ee3t, kh\u00f4ng n\u1ed1i b\u1eb1ng \u0111o\u1ea1n th\u1eb3ng.\"}},\n{\"@type\":\"Question\",\"name\":\"Parabol c\u00f3 \u1ee9ng d\u1ee5ng g\u00ec trong th\u1ef1c t\u1ebf?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Parabol xu\u1ea5t hi\u1ec7n trong qu\u1ef9 \u0111\u1ea1o v\u1eadt b\u1ecb n\u00e9m xi\u00ean, thi\u1ebft k\u1ebf g\u01b0\u01a1ng c\u1ea7u, \u0103ng-ten parabol gi\u00fap h\u1ed9i t\u1ee5 t\u00edn hi\u1ec7u v\u1ec1 m\u1ed9t \u0111i\u1ec3m, hay h\u00ecnh d\u00e1ng d\u00e2y v\u0103ng c\u1ee7a m\u1ed9t s\u1ed1 c\u00e2y c\u1ea7u.\"}}\n]}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Parabol l\u00e0 d\u1ea1ng \u0111\u1ed3 th\u1ecb h\u00ecnh ch\u1eef U quen thu\u1ed9c m\u00e0 b\u1ea1n g\u1eb7p ngay t\u1eeb nh\u1eefng b\u00e0i \u0111\u1ea7u ti\u00ean v\u1ec1 h\u00e0m s\u1ed1 b\u1eadc hai \u1edf l\u1edbp 9, l\u1edbp 10. Kh\u00f4ng ch\u1ec9 l\u00e0 ki\u1ebfn th\u1ee9c thi c\u1eed, parabol c\u00f2n xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u hi\u1ec7n t\u01b0\u1ee3ng th\u1ef1c t\u1ebf nh\u01b0 qu\u1ef9 \u0111\u1ea1o m\u1ed9t v\u1eadt \u0111\u01b0\u1ee3c n\u00e9m l\u00ean, h\u00ecnh [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":568869,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"parabol l\u00e0 g\u00ec","_yoast_wpseo_title":"Parabol l\u00e0 g\u00ec? \u0110\u1ec9nh, tr\u1ee5c \u0111\u1ed1i x\u1ee9ng, c\u00e1ch v\u1ebd","_yoast_wpseo_metadesc":"Parabol l\u00e0 g\u00ec? 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