{"id":257,"date":"2020-04-15T10:56:00","date_gmt":"2020-04-15T08:56:00","guid":{"rendered":"http:\/\/public.kvcso.cz\/?p=257"},"modified":"2022-04-04T22:31:50","modified_gmt":"2022-04-04T20:31:50","slug":"kvadraticke-rovnice-v-geogebre","status":"publish","type":"post","link":"https:\/\/ucitel.kvcso.cz\/?p=257","title":{"rendered":"Kvadratick\u00e9 rovnice v Geogeb\u0159e"},"content":{"rendered":"\n

Jde o grafick\u00e9 \u0159e\u0161en\u00ed rovnic a vizualizaci pomoc\u00ed rozhran\u00ed nebo aplikace Geogebra<\/em>. Z\u00e1le\u017e\u00ed na tom, jestli pracuji v prohl\u00ed\u017ee\u010di, nebo na tabletu. Pro mne je v tuto chv\u00edli asi nejlep\u0161\u00ed tvorba videa na iPadu<\/em>, proto\u017ee nevy\u017eaduje \u017e\u00e1dn\u00e9 doprovodn\u00e9 instalace. Sta\u010d\u00edm si pouze s tabletem. Geogebru pou\u017e\u00edv\u00e1m b\u011b\u017en\u011b a tak jde o vytvo\u0159en\u00ed videa. Prakticky vlastn\u011b jen o sn\u00edm\u00e1n\u00ed obrazovky.<\/p>\n\n\n\n

Vysv\u011btlen\u00ed grafick\u00e9ho \u0159e\u0161en\u00ed kvadratick\u00fdch rovnic jsem provedl ve \u0161kole p\u0159i b\u011b\u017en\u00e9 v\u00fduce. Co\u017e je velk\u00e1 v\u00fdhoda, proto\u017ee se m\u00e1m od \u010deho odrazit. Vlastn\u011b pracuji jen s parametry rovnice, resp. porovn\u00e1v\u00e1n\u00edm funk\u010dn\u00edch hodnot kvadratick\u00e9 a konstantn\u00ed funkce a hled\u00e1n\u00edm, pro jak\u00e9 x<\/em> to plat\u00ed.<\/p>\n\n\n\n

y = ax2<\/sup> + bx + c
y = 0

<\/strong>Je mo\u017en\u00e9 vyu\u017e\u00edt i line\u00e1rn\u00ed funkci a u kvadratick\u00e9 pracovat jen s \u010dlenem ax2<\/sup>. J\u00e1 tento p\u0159\u00edklad pou\u017e\u00edv\u00e1m tak\u00e9, sp\u00ed\u0161e ale jako alternativn\u00ed \u0159e\u0161en\u00ed, proto\u017ee pro pochopen\u00ed je jednodu\u0161\u0161\u00ed hled\u00e1n\u00ed pr\u016fse\u010d\u00edk\u016f s konstantn\u00ed funkc\u00ed. P\u0159\u00edprava v Geogeb\u0159e je snadn\u00e1, pot\u00e9 ji\u017e sta\u010d\u00ed promyslet postup pro vysv\u011btlen\u00ed a spustit nahr\u00e1v\u00e1n\u00ed.<\/p>\n\n\n\n

iPad je pro kantora skv\u011bl\u00e1 pom\u016fcka. Pou\u017e\u00edv\u00e1m jej t\u00e9m\u011b\u0159 8 let a sna\u017e\u00edm se, aby mi nahrazoval notebook maxim\u00e1ln\u011b mo\u017en\u011b. \u00dapln\u011b to nejde, ale toto je p\u0159esn\u011b situace, kdy ne\u0159e\u0161\u00edm dostupnost v\u0161ech pot\u0159ebn\u00fdch n\u00e1stroj\u016f a mohu hned tvo\u0159it. I kdy\u017e m\u00e1m u \u017e\u00e1k\u016f u podobn\u00fdch \u00faloh r\u00e1d chromebooky nebo mobily, pro mne jako mentora v\u00fduky je iPad flexibiln\u011bj\u0161\u00ed za\u0159\u00edzen\u00ed.<\/p>\n\n\n\n

Video nen\u00ed samo\u00fa\u010deln\u00e9, ale m\u00e1m jej za\u0159azen\u00e9 v kurzu v Classroomu jako sou\u010d\u00e1st dal\u0161\u00edch materi\u00e1l\u016f v\u010detn\u011b doprovodn\u00fdch text\u016f. A p\u0159edev\u0161\u00edm i jako zdroj pro \u00fakol. Je to vlastn\u011b opravdu jednoduch\u00e9. V\u00fdhoda je, \u017ee m\u016f\u017eu vytvo\u0159it v\u00edce inspirativn\u00edch ot\u00e1zek, kter\u00e9 se t\u00fdkaj\u00ed dynami\u010dnosti parametr\u016f a, b, c<\/em>. Ve stylu: „Co nastane, kdy\u017e \u2026?“<\/em>.<\/p>\n\n\n\n


Videouk\u00e1zka<\/a><\/p>\n\n\n\n

\"Geogebra\"<\/figure><\/div>\n\n\n\n

Kvadratick\u00e1 a konstantn\u00ed funkce – sou\u0159adnice x u obou bod\u016f je \u0159e\u0161en\u00edm rovnice<\/em><\/p>\n\n\n\n

<\/p>\n\n\n\n

\"Geogebra\"<\/figure><\/div>\n\n\n\n

Kvadratick\u00e1 a line\u00e1rn\u00ed funkce – sou\u0159adnice x u obou bod\u016f je \u0159e\u0161en\u00edm rovnice<\/em><\/p>\n\n\n\n

Autor: Petr Chlebek <\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Jde o grafick\u00e9 \u0159e\u0161en\u00ed rovnic a vizualizaci pomoc\u00ed rozhran\u00ed nebo aplikace Geogebra. Z\u00e1le\u017e\u00ed na tom, jestli pracuji v prohl\u00ed\u017ee\u010di, nebo na tabletu. Pro mne je v tuto chv\u00edli asi nejlep\u0161\u00ed tvorba videa na iPadu, proto\u017ee nevy\u017eaduje \u017e\u00e1dn\u00e9 doprovodn\u00e9 instalace. Sta\u010d\u00edm si pouze s tabletem. Geogebru pou\u017e\u00edv\u00e1m b\u011b\u017en\u011b a tak jde o vytvo\u0159en\u00ed videa. Prakticky vlastn\u011b jen o…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,7],"tags":[70,108,37,15,34],"class_list":["post-257","post","type-post","status-publish","format-standard","hentry","category-sekce-ict","category-sekce-matematiky-a-informatiky","tag-classroom","tag-digitalni-kompetence-2","tag-geogebra","tag-ict","tag-matematika"],"_links":{"self":[{"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/posts\/257","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=257"}],"version-history":[{"count":4,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/posts\/257\/revisions"}],"predecessor-version":[{"id":374,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=\/wp\/v2\/posts\/257\/revisions\/374"}],"wp:attachment":[{"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=257"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=257"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ucitel.kvcso.cz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=257"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}