{"id":3183,"date":"2022-05-31T21:22:21","date_gmt":"2022-05-31T19:22:21","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/parabola-vrcholova-rovnice\/"},"modified":"2022-05-31T21:52:59","modified_gmt":"2022-05-31T19:52:59","slug":"parabola-vrcholova-rovnice","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/parabola-vrcholova-rovnice\/","title":{"rendered":"Parabola &#8211; vrcholov\u00e1 a obecn\u00e1 rovnice"},"content":{"rendered":"<ul>\n<li><strong>Parabola m\u016f\u017ee m\u00edt 4 r\u016fzn\u00e9 podoby:<\/strong><\/li>\n<\/ul>\n<ol>\n<li><strong>tvar \u222a:<\/strong> osa paraboly je<strong> rovnob\u011b\u017en\u00e1 s osou y<\/strong> a je<strong> omezen\u00e1 zdola<\/strong><\/li>\n<li><strong>tvar \u2229:<\/strong> osa paraboly je <strong>rovnob\u011b\u017en\u00e1 s osou y<\/strong> a je <strong>omezen\u00e1 shora<\/strong><\/li>\n<li><strong>tvar \u2282:<\/strong> osa paraboly je<strong> rovnob\u011b\u017en\u00e1 s osou x<\/strong> a je <strong>omezen\u00e1 zleva<\/strong><\/li>\n<li><strong>tvar \u2283:<\/strong> osa paraboly je<strong> rovnob\u011b\u017en\u00e1 s osou x<\/strong> a je <strong>omezen\u00e1 zprava<\/strong><\/li>\n<\/ol>\n<ul>\n<li><strong>Vrcholov\u00e1 rovnice paraboly<\/strong><\/li>\n<\/ul>\n<p>li\u0161\u00ed se v z\u00e1vislosti na tvaru paraboly (ka\u017ed\u00e1 ze 4 podob m\u00e1 jinou vrcholovou rovnici)<\/p>\n<p>Vrchol <strong>V<\/strong> m\u00e1 <strong>v\u017edy<\/strong> sou\u0159adnice <strong>[m, n]<\/strong>, sou\u0159adnice ohniska se li\u0161\u00ed v z\u00e1vislosti na tvaru paraboly<\/p>\n<p style=\"text-align: center\"><strong>Vrcholov\u00e1 rovnice pro parabolu ve tvaru \u222a <\/strong>(osa paraboly je<strong> rovnob\u011b\u017en\u00e1 s osou y<\/strong> a je<strong> omezen\u00e1 zdola)<\/strong><\/p>\n<p style=\"text-align: center\">ohnisko <strong><em>F<\/em><\/strong> m\u00e1 sou\u0159adnice:<\/p>\n<p style=\"text-align: center\">$$F\\left[m, n+\\frac{p}{2}\\right]$$<\/p>\n<p style=\"text-align: center\"><strong>vrcholov\u00e1 rovnice:<\/strong><\/p>\n<p style=\"text-align: center\">$$(x-m)^2=2p(y-n)$$<\/p>\n<p style=\"text-align: center\"><strong>Vrcholov\u00e1 rovnice pro parabolu ve tvaru \u2229 (<\/strong>osa paraboly<strong> je rovnob\u011b\u017en\u00e1 s osou y <\/strong>a je <strong>omezen\u00e1 shora)<\/strong><\/p>\n<p style=\"text-align: center\">ohnisko <strong><em>F<\/em><\/strong> m\u00e1 sou\u0159adnice:<\/p>\n<p style=\"text-align: center\">$$F\\left[m,n-\\frac{p}{2}\\right]$$<\/p>\n<p style=\"text-align: center\"><strong>vrcholov\u00e1 rovnice:<\/strong><\/p>\n<p style=\"text-align: center\">$$(x-m)^2=-2p(y-n)$$<\/p>\n<p style=\"text-align: center\"><strong>Vrcholov\u00e1 rovnice pro parabolu ve tvaru\u00a0<\/strong><strong>\u2282 <\/strong>(osa paraboly je<strong> rovnob\u011b\u017en\u00e1 s osou x<\/strong> a je <strong>omezen\u00e1 zleva)<\/strong><\/p>\n<p style=\"text-align: center\">ohnisko <strong><em>F<\/em><\/strong> m\u00e1 sou\u0159adnice:<\/p>\n<p style=\"text-align: center\">$$F\\left[m+\\frac{p}{2},n\\right]$$<\/p>\n<p style=\"text-align: center\"><strong>vrcholov\u00e1 rovnice:<\/strong><\/p>\n<p style=\"text-align: center\">$$(y-n)^2=2p(x-m)$$<\/p>\n<p style=\"text-align: center\"><strong>Vrcholov\u00e1 rovnice pro parabolu ve tvaru<\/strong><strong>\u2283 <\/strong>(osa paraboly je<strong> rovnob\u011b\u017en\u00e1 s osou x<\/strong> a je <strong>omezen\u00e1 zprava<\/strong>)<\/p>\n<p style=\"text-align: center\">ohnisko <strong><em>F<\/em><\/strong> m\u00e1 sou\u0159adnice:<\/p>\n<p style=\"text-align: center\">$$F\\left[m-\\frac{p}{2},n\\right]$$<\/p>\n<p style=\"text-align: center\"><strong>vrcholov\u00e1 rovnice:<\/strong><\/p>\n<p style=\"text-align: center\">$$(y-n)^2=-2p(x-m)$$<\/p>\n<ul>\n<li><strong>Obecn\u00e1 rovnice paraboly vznikne rozn\u00e1soben\u00edm vrcholov\u00e9 rovnice<\/strong><\/li>\n<\/ul>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-3183","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - 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