{"id":110248,"date":"2020-01-29T18:14:40","date_gmt":"2020-01-29T17:14:40","guid":{"rendered":"https:\/\/www.superprof.es\/diccionario\/calculo\/parabola.html"},"modified":"2026-10-07T17:44:03","modified_gmt":"2026-10-07T15:44:03","slug":"parabola","status":"publish","type":"post","link":"https:\/\/www.superprof.es\/diccionario\/matematicas\/calculo\/parabola.html","title":{"rendered":"Par\u00e1bola"},"content":{"rendered":"<section id=\"sec\" style=\"\">\r\n          \n\n<p class=\"wp-block-paragraph\">Una <strong>par\u00e1bola es <\/strong>la <strong>representaci\u00f3n gr\u00e1fica<\/strong> de una <strong>funci\u00f3n cuadr\u00e1tica<\/strong>.<\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>f(x) = ax\u00b2 + bx +c <\/strong><\/p>\n\n\r\n                            \n\n<h2 class=\"wp-block-heading\">Representaci\u00f3n gr\u00e1fica de una par\u00e1bola<\/h2>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Se puede representar  una <strong>par\u00e1bola<\/strong> a partir de estos puntos:<\/p>\n\n\r\n                            \n\n<h3 class=\"wp-block-heading\">1. V\u00e9rtice<\/h3>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-1.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 1\"  ><\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Por este punto pasa el <strong>eje de simetr\u00eda de la par\u00e1bola<\/strong>. <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">La ecuaci\u00f3n del <strong>eje de simetr\u00eda<\/strong> es:<\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"> <img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-2.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 2\"  ><\/p>\n\n\r\n                            \n\n<h3 class=\"wp-block-heading\">2. Puntos de corte con el eje OX.<\/h3>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">En el eje de abscisas la segunda coordenada es cero, por lo que tendremos:<\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>ax\u00b2 + bx +c = 0<\/strong><\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Resolviendo la ecuaci\u00f3n podemos obtener: <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>Dos puntos de corte: <span class=\"sol\">(x<sub>1<\/sub>, 0) y (x<sub>2<\/sub>, 0)<\/span> si  b\u00b2 - 4ac > 0 <\/strong><\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>Un punto de corte: <span class=\"esmeralda\">(x<sub>1<\/sub>, 0)<\/span> si  b\u00b2 - 4ac = 0 <\/strong> <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>Ning\u00fan punto de corte si   b\u00b2 - 4ac < 0 <\/strong><\/p>\n\n\r\n                            \n\n<h3 class=\"wp-block-heading\">3. Punto de corte con el eje OY. <\/h3>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">En el eje de ordenadas la primera coordenada es cero, por lo que tendremos:<\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><strong>f(0) = a\u00b7 0\u00b2 + b\u00b7 0 +c = c<\/strong>        <span class=\"Estilo3\"><span class=\"sol\">(0,c) <\/span><\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br \/><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> Representar la funci\u00f3n f(x) = x\u00b2 - 4x + 3<\/p>\n\n\r\n                            \n\n<h2 class=\"wp-block-heading\">1. V\u00e9rtice<\/h2>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">x<sub> v <\/sub> = - (-4) \/ 2 = 2     y<sub> v <\/sub>= 2\u00b2 - 4\u00b7 2 + 3 = -1       <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"> <span class=\"sol\">V(2, -1)<\/span><\/p>\n\n\r\n                            \n\n<h2 class=\"wp-block-heading\">2. Puntos de corte con el eje OX.<\/h2>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">x\u00b2 - 4x + 3 = 0 <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-3.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 3\" \/>       <\/p>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><span class=\"sol\">(3, 0)      (1, 0)<\/span><\/p>\n\n\r\n                            \n\n<h2 class=\"wp-block-heading\">3. Punto de corte con el eje OY.<\/h2>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\"><span class=\"sol\">(0, 3)<\/span><\/p>\n\n\r\n              \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-4.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 4\"  ><\/p>\n\n\r\n\r\n                            \r\n              \n\n<h2 class=\"wp-block-heading\">Traslaciones de par\u00e1bolas<\/h2>\n\n\r\n                            \n\n<p class=\"wp-block-paragraph\">Tambi\u00e9n podemos representar <strong>par\u00e1bolas <\/strong>a partir de las <strong>traslaciones<\/strong> de la funci\u00f3n: <strong>y = x\u00b2<\/strong>.<\/p>\n\n\r\n                            \r\n                          \r\n                            <table class=\"responsive sbc\" data-min=\"8\" data-max=\"12\">\r\n                              <tr>\r\n                                <th>x<\/th>\r\n                                <th style=\"vertical-align:bottom\">y = x\u00b2<\/th>\r\n                              <\/tr>\r\n                              <tr>\r\n                                <td>-2<\/td>\r\n                                <td style=\"text-align:center\">4<\/td>\r\n                              <\/tr>\r\n                              <tr>\r\n                                <td>-1<\/td>\r\n                                <td style=\"text-align:center\">1<\/td>\r\n                              <\/tr>\r\n                              <tr>\r\n                                <td>0<\/td>\r\n                                <td style=\"text-align:center\">0<\/td>\r\n                              <\/tr>\r\n                              <tr>\r\n                                <td>1<\/td>\r\n                                <td style=\"text-align:center\">1<\/td>\r\n                              <\/tr>\r\n                              <tr>\r\n                                <td>2<\/td>\r\n                                <td style=\"text-align:center\">4<\/td>\r\n                              <\/tr>\r\n                            <\/table>\r\n                        \r\n\t\t\t\t\t\t\n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-5.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 5\" \/><\/p>\n\n\r\n\t\t\t\t\t\t \r\n                        \n\n<h3 class=\"wp-block-heading\">1. Traslaci\u00f3n vertical<\/h3>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><strong>y = x\u00b2 + k <\/strong><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">Si <strong>K > 0<\/strong>, y = x\u00b2 se desplaza hacia <strong>arriba k unidades<\/strong>.<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">Si <strong>K < 0<\/strong>, y = x\u00b2 se desplaza hacia <strong>abajo k unidades<\/strong>.<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">El <strong>v\u00e9rtice de la par\u00e1bola<\/strong> es: <strong>(0, k)<\/strong>. <\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"> El <strong>eje de simetr\u00eda x = 0<\/strong>.<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-6.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 6\"  height=\"312\" style=\"margin-left:10%;\" \/><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-7.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 7\" width=\"192\" \/><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><strong><span class=\"sol\">y = x\u00b2 +2 <\/span> <\/strong><span class=\"sol\" style=\"margin-left:20%;\"><strong>y = x\u00b2 -2<\/strong><\/span><\/p>\n\n\r\n                        \n\n<h3 class=\"wp-block-heading\">2. Traslaci\u00f3n horizontal <\/h3>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><strong>y = (x + h)\u00b2 <\/strong><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">Si <strong>h > 0<\/strong>, y = x\u00b2 se desplaza hacia la <strong>izquierda h unidades<\/strong>.<\/p>\n\n\r\n                      \n\n<p class=\"wp-block-paragraph\">Si<strong> h < 0<\/strong>, y = x\u00b2 se desplaza hacia la <strong>derecha h unidades<\/strong>.<\/p>\n\n\r\n                      \n\n<p class=\"wp-block-paragraph\">El <strong>v\u00e9rtice de la par\u00e1bola<\/strong> es: <strong>(-h, 0)<\/strong>.<\/p>\n\n\r\n                      \n\n<p class=\"wp-block-paragraph\">El <strong>eje de simetr\u00eda<\/strong> es <strong>x = -h<\/strong>. <\/p>\n\n\r\n                      \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-8.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 8\"  height=\"290\" style=\"margin-left:10%;\" \/><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-9.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 9\" width=\"218\" \/><\/p>\n\n\r\n                      \n\n<p class=\"wp-block-paragraph\"><span class=\"sol\" style=\"margin-left:10%;\">y = (x + 2)\u00b2<\/span><span class=\"sol\" style=\"margin-left:20%;\">y = (x - 2)\u00b2<\/span><\/p>\n\n\r\n                        \n\n<h3 class=\"wp-block-heading\">3. Traslaci\u00f3n oblicua<\/h3>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"> <strong>y = (x + h)\u00b2 + k<\/strong><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><strong>El v\u00e9rtice de la par\u00e1bola es: (-h, k)<\/strong>.<\/p>\n\n\r\n                      \n\n<p class=\"wp-block-paragraph\"> <strong>El eje de simetr\u00eda es x = -h. <\/strong><\/p>\n\n\r\n                     \r\n                        \n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-10.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 10\"  height=\"300\" style=\"margin-left:10%;\" \/><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/par&aacute;bola-11.gif\" alt=\"Explicaciones y ejemplos de par&aacute;bola - 11\" width=\"222\" \/><\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\"><span class=\"sol\" style=\"margin-left:10%;\">y = (x - 2)\u00b2 + 2<\/span> <span class=\"sol\" style=\"margin-left:20%;\">y = (x + 2)\u00b2 \u2212 2<\/span> <\/p>\n\n\n<\/section>","protected":false},"excerpt":{"rendered":"<p>Una par\u00e1bola es la representaci\u00f3n gr\u00e1fica de una funci\u00f3n cuadr\u00e1tica. f(x) = ax\u00b2 + bx +c Representaci\u00f3n gr\u00e1fica de una par\u00e1bola Se puede representar una par\u00e1bola a partir de estos puntos: 1. V\u00e9rtice Por este punto pasa el eje de simetr\u00eda de la par\u00e1bola. La ecuaci\u00f3n del eje de simetr\u00eda es: 2. Puntos de corte [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","footnotes":""},"categories":[366],"tags":[363],"class_list":["post-110248","post","type-post","status-publish","format-standard","hentry","category-calculo","tag-p"],"acf":[],"author_meta":{"display_name":"Andra","author_link":"https:\/\/www.superprof.es\/diccionario\/author\/andra"},"featured_img":null,"coauthors":[],"tax_additional":{"categories":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/calculo\" class=\"advgb-post-tax-term\">C\u00e1lculo<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">C\u00e1lculo<\/span>"]},"tags":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/calculo\" class=\"advgb-post-tax-term\">p<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">p<\/span>"]}},"comment_count":"0","relative_dates":{"created":"Publicado 7 a\u00f1os hace","modified":"Actualizado 4 semanas hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 7 octubre 2026"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 14 min","modified":"Actualizado el 7 octubre 2026 17 h 44 min"},"featured_img_caption":"","series_order":"","_links":{"self":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/110248","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/comments?post=110248"}],"version-history":[{"count":6,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/110248\/revisions"}],"predecessor-version":[{"id":141729,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/110248\/revisions\/141729"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=110248"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=110248"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=110248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}