[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.01,0:00:04.52,Default,,0000,0000,0000,,Vitam vas na prednaske o kvadratickej rovnici.
Dialogue: 0,0:00:04.52,0:00:06.73,Default,,0000,0000,0000,,Taka kvadraticka rovnica, to znie ako nieco
Dialogue: 0,0:00:06.73,0:00:07.81,Default,,0000,0000,0000,,velmi zlozite.
Dialogue: 0,0:00:07.81,0:00:09.93,Default,,0000,0000,0000,,Ked skutocne prvykrat uvidite kvadraticku rovnicu,
Dialogue: 0,0:00:09.93,0:00:11.59,Default,,0000,0000,0000,,poviete si, nielenze to znie
Dialogue: 0,0:00:11.59,0:00:13.11,Default,,0000,0000,0000,,zlozito, ale to a jzlozite je.
Dialogue: 0,0:00:13.11,0:00:14.93,Default,,0000,0000,0000,,Nastastie vsak v priebehu tejto prednasky uvidite,
Dialogue: 0,0:00:14.93,0:00:16.58,Default,,0000,0000,0000,,ze to v skutocnosti nie je take tazke.
Dialogue: 0,0:00:16.58,0:00:19.04,Default,,0000,0000,0000,,V buducej prednaske vam ukazem,
Dialogue: 0,0:00:19.04,0:00:21.30,Default,,0000,0000,0000,,ako to bolo odvodene.
Dialogue: 0,0:00:21.30,0:00:24.81,Default,,0000,0000,0000,,Vo vseobecnosti ste sa uz naucili rozlozit
Dialogue: 0,0:00:24.81,0:00:25.81,Default,,0000,0000,0000,,rovnicu druheho stupna.
Dialogue: 0,0:00:25.81,0:00:30.91,Default,,0000,0000,0000,,Naucili ste sa, ze ak som mal, povedzme, x na druhu,
Dialogue: 0,0:00:30.91,0:00:40.34,Default,,0000,0000,0000,,minus x, minus 6, rovna sa 0.
Dialogue: 0,0:00:40.34,0:00:42.97,Default,,0000,0000,0000,,Ak by som mal taku rovnicu, x na druhu minus x minus x sa rovna
Dialogue: 0,0:00:42.97,0:00:48.72,Default,,0000,0000,0000,,nula, mohli by ste ju rozlozit ako x minus 3 a
Dialogue: 0,0:00:48.72,0:00:52.21,Default,,0000,0000,0000,,x plus 2 rovna sa 0.
Dialogue: 0,0:00:52.21,0:00:54.96,Default,,0000,0000,0000,,Staci, ak x minus 3 sa rovna 0, alebo
Dialogue: 0,0:00:54.96,0:00:57.07,Default,,0000,0000,0000,,x plus 2 sa rovna 0.
Dialogue: 0,0:00:57.07,0:01:03.51,Default,,0000,0000,0000,,Takze x minus 3 sa rovna 0 alebo x plus 2 sa rovna 0.
Dialogue: 0,0:01:03.51,0:01:08.50,Default,,0000,0000,0000,,Takze x sa rovna 3 alebo minus 2.
Dialogue: 0,0:01:08.50,0:01:17.98,Default,,0000,0000,0000,,Graficke zobrazenie tohto by bolo, ak by som mal
Dialogue: 0,0:01:17.98,0:01:26.15,Default,,0000,0000,0000,,funkciu f (x) sa rovna x na druhu minus x minus 6.
Dialogue: 0,0:01:26.15,0:01:28.76,Default,,0000,0000,0000,,Tato os je f osi x.
Dialogue: 0,0:01:28.76,0:01:32.67,Default,,0000,0000,0000,,Mozno ti je znamejsia os y, ale na ucely
Dialogue: 0,0:01:32.67,0:01:34.78,Default,,0000,0000,0000,,nasho problemu na tom nezalezi.
Dialogue: 0,0:01:34.78,0:01:36.27,Default,,0000,0000,0000,,Toto je os x.
Dialogue: 0,0:01:36.27,0:01:40.43,Default,,0000,0000,0000,,Ak by som chcel znazornit tuto rovnicu, x na druhu minus x,
Dialogue: 0,0:01:40.43,0:01:42.38,Default,,0000,0000,0000,,minus 6, vyzeralo by to asi takto.
Dialogue: 0,0:01:42.38,0:01:50.13,Default,,0000,0000,0000,,Trochu ako -- toto je f (x) rovna sa minus 6.
Dialogue: 0,0:01:50.13,0:01:52.90,Default,,0000,0000,0000,,Graf by vyzeral asi takto.
Dialogue: 0,0:01:52.90,0:01:57.15,Default,,0000,0000,0000,,Pojde to smerom hore.
Dialogue: 0,0:02:00.03,0:02:03.15,Default,,0000,0000,0000,,Vedz, ze to ide cez minus 6, pretoze ked sa x rovna 0,
Dialogue: 0,0:02:03.15,0:02:05.11,Default,,0000,0000,0000,,f (x) sa rovna minus 6.
Dialogue: 0,0:02:05.11,0:02:07.80,Default,,0000,0000,0000,,Takto ja viem, ze to ide cez tento bod.
Dialogue: 0,0:02:07.80,0:02:11.52,Default,,0000,0000,0000,,Viem aj, ze ked f(x) sa rovna 0, tak f(x) sa rovna
Dialogue: 0,0:02:11.52,0:02:14.96,Default,,0000,0000,0000,,0 pozdlz celej osi x. spravne?
Dialogue: 0,0:02:14.96,0:02:16.60,Default,,0000,0000,0000,,Tu je 1.
Dialogue: 0,0:02:16.60,0:02:17.87,Default,,0000,0000,0000,,Tu je 0.
Dialogue: 0,0:02:17.87,0:02:19.16,Default,,0000,0000,0000,,Tu je minus 1.
Dialogue: 0,0:02:19.16,0:02:21.51,Default,,0000,0000,0000,,Takze tu to je, kde f(x) sa rovna 0, na
Dialogue: 0,0:02:21.51,0:02:23.42,Default,,0000,0000,0000,,celej tejto osi x, spravne?
Dialogue: 0,0:02:23.42,0:02:29.21,Default,,0000,0000,0000,,Vieme, ze to sa rovna 0 v bodoch, kde x sa rovna 3 a
Dialogue: 0,0:02:29.21,0:02:32.33,Default,,0000,0000,0000,,x sa rovna minus 2.
Dialogue: 0,0:02:32.33,0:02:34.36,Default,,0000,0000,0000,,Toto je vlastne to, co sme tu riesili.
Dialogue: 0,0:02:34.36,0:02:36.44,Default,,0000,0000,0000,,Mozno ked sme sa venovali problemom s rozlozenim,
Dialogue: 0,0:02:36.44,0:02:38.94,Default,,0000,0000,0000,,neuvedomili sme si graficky, co robime.
Dialogue: 0,0:02:38.94,0:02:42.07,Default,,0000,0000,0000,,Ale ak sme si povedali, ze f(x) sa rovna tejto funkcii,
Dialogue: 0,0:02:42.07,0:02:43.27,Default,,0000,0000,0000,,prisudzujeme jej hodnotu nula.
Dialogue: 0,0:02:43.27,0:02:44.82,Default,,0000,0000,0000,,Hovorime tomu funkcia. Kedy sa
Dialogue: 0,0:02:44.82,0:02:48.22,Default,,0000,0000,0000,,tato funkcia rovna 0?
Dialogue: 0,0:02:48.22,0:02:49.39,Default,,0000,0000,0000,,kedy?
Dialogue: 0,0:02:49.39,0:02:51.72,Default,,0000,0000,0000,,Rovna sa nule v tychto bodoch, ano?
Dialogue: 0,0:02:51.72,0:02:55.36,Default,,0000,0000,0000,,Pretoze tu sa f(x) rovna 0.
Dialogue: 0,0:02:55.36,0:02:57.49,Default,,0000,0000,0000,,Ked sme toto vyriesili
Dialogue: 0,0:02:57.49,0:03:01.97,Default,,0000,0000,0000,,rozlozenim, prisli sme na to, ze hodnoty x, ktore tvorili f(x),
Dialogue: 0,0:03:01.97,0:03:04.16,Default,,0000,0000,0000,,sa rovnaju 0, co su tieto dva body.
Dialogue: 0,0:03:04.16,0:03:06.74,Default,,0000,0000,0000,,Teraz trocha terminologie - nazyvaju sa
Dialogue: 0,0:03:06.74,0:03:09.86,Default,,0000,0000,0000,,nulami, alebo aj korenmi f(x).
Dialogue: 0,0:03:09.86,0:03:12.47,Default,,0000,0000,0000,,Trocha si to zopakujme.
Dialogue: 0,0:03:14.81,0:03:23.70,Default,,0000,0000,0000,,Ak by som mal nieco ako f(x) sa rovna x na druhu plus
Dialogue: 0,0:03:23.70,0:03:29.55,Default,,0000,0000,0000,,4 krat x plus 4, a opytal by som sa ta, kde su nuly ci
Dialogue: 0,0:03:29.55,0:03:31.77,Default,,0000,0000,0000,,korene f(x)?
Dialogue: 0,0:03:31.77,0:03:33.97,Default,,0000,0000,0000,,To je to iste, ako opytat sa ta: kde f(x)
Dialogue: 0,0:03:33.97,0:03:36.30,Default,,0000,0000,0000,,pretina os x?
Dialogue: 0,0:03:36.30,0:03:38.21,Default,,0000,0000,0000,,Pretina ju, ked f(x)
Dialogue: 0,0:03:38.21,0:03:39.44,Default,,0000,0000,0000,,sa rovna 0, ano?
Dialogue: 0,0:03:39.44,0:03:42.12,Default,,0000,0000,0000,,Ak teda myslime graf, ktory som predtym nakreslil.
Dialogue: 0,0:03:42.12,0:03:45.72,Default,,0000,0000,0000,,Povedzme, ze f(x) sa rovna 0, potom mozeme
Dialogue: 0,0:03:45.72,0:03:51.86,Default,,0000,0000,0000,,povedat, ze 0 sa rovna x na druhu plus 4 krat x plus 4.
Dialogue: 0,0:03:51.86,0:03:53.94,Default,,0000,0000,0000,,Vieme, ze to mozeme rozlozit, teda x
Dialogue: 0,0:03:53.94,0:03:57.08,Default,,0000,0000,0000,,plus 2 krat x plus 2.
Dialogue: 0,0:03:57.08,0:04:07.09,Default,,0000,0000,0000,,Vieme, ze sa to rovna 0, ak sa x rovna minus 2.
Dialogue: 0,0:04:07.09,0:04:10.17,Default,,0000,0000,0000,,x sa rovna minus 2.
Dialogue: 0,0:04:13.94,0:04:18.27,Default,,0000,0000,0000,,No, toto je trocha preklep, takze x sa rovna minus 2.
Dialogue: 0,0:04:18.27,0:04:22.38,Default,,0000,0000,0000,,Tak teraz uz vieme, ako najdeme korene, ked sa urcita
Dialogue: 0,0:04:22.38,0:04:24.56,Default,,0000,0000,0000,,rovnica da lahko rozlozit.
Dialogue: 0,0:04:24.56,0:04:27.50,Default,,0000,0000,0000,,Ale skusme rovnicu, ktoru nie je v skutocnosti
Dialogue: 0,0:04:27.50,0:04:28.85,Default,,0000,0000,0000,,take lahke rozlozit.
Dialogue: 0,0:04:28.85,0:04:32.12,Default,,0000,0000,0000,,Priklad: mame f(x) sa rovna minus 10 krat x
Dialogue: 0,0:04:39.75,0:04:45.38,Default,,0000,0000,0000,,na druhu minus 9 krat x plus 1.
Dialogue: 0,0:04:45.38,0:04:47.58,Default,,0000,0000,0000,,Ked sa na to pozriem, aj keby som to vydelil 10,
Dialogue: 0,0:04:47.58,0:04:48.65,Default,,0000,0000,0000,,ostali by mi tu nejake zlomky.
Dialogue: 0,0:04:48.65,0:04:53.13,Default,,0000,0000,0000,,Je velmi tazke predstavit si rozlozenie tejto kvadratickej rovnice.
Dialogue: 0,0:04:53.13,0:04:54.86,Default,,0000,0000,0000,,Toto sa vlastne vola kvadraticka rovnica, alebo
Dialogue: 0,0:04:54.86,0:04:57.58,Default,,0000,0000,0000,,druhostupnovy polynomial.
Dialogue: 0,0:04:57.58,0:04:59.60,Default,,0000,0000,0000,,Skusime to vyriesit.
Dialogue: 0,0:04:59.60,0:05:02.42,Default,,0000,0000,0000,,Pretoze chceme zistit, kedy sa to rovna 0.
Dialogue: 0,0:05:02.42,0:05:07.13,Default,,0000,0000,0000,,Minus 10 krat x na druhu minus 9 krat x plus 1.
Dialogue: 0,0:05:07.13,0:05:09.09,Default,,0000,0000,0000,,Chceme zistit, ake hodnoty musi mat x, aby
Dialogue: 0,0:05:09.09,0:05:11.26,Default,,0000,0000,0000,,sa tato rovnica rovnala 0.
Dialogue: 0,0:05:11.26,0:05:13.73,Default,,0000,0000,0000,,A tu mozme pouzit pomocku nazvanu vzorec kvadratickej\Nrovnice.
Dialogue: 0,0:05:13.73,0:05:15.62,Default,,0000,0000,0000,,Teraz vam dam jednu radu v matematike,
Dialogue: 0,0:05:15.62,0:05:18.03,Default,,0000,0000,0000,,ktoru je dobre si zapamatat.
Dialogue: 0,0:05:18.03,0:05:21.33,Default,,0000,0000,0000,,Korene kvadratickej rovnice sa vypocitaju podla \Ndaneho vzorca.
Dialogue: 0,0:05:21.33,0:05:24.81,Default,,0000,0000,0000,,Kvadraticka rovnica ma vo vseobecnosti takyto tvar:
Dialogue: 0,0:05:24.81,0:05:31.90,Default,,0000,0000,0000,,A krat x na druhu plus B krat x plus C sa rovna 0.
Dialogue: 0,0:05:31.90,0:05:35.79,Default,,0000,0000,0000,,V nasom priklade je A minus 10,
Dialogue: 0,0:05:35.79,0:05:39.94,Default,,0000,0000,0000,,B je minus 9, a C je 1.
Dialogue: 0,0:05:39.94,0:05:48.04,Default,,0000,0000,0000,,Vzorec je: korene x sa rovnaju minus B plus alebo minus
Dialogue: 0,0:05:48.04,0:05:58.06,Default,,0000,0000,0000,,druha odmocnina B na druhu minus 4 krat A krat C,
Dialogue: 0,0:05:58.06,0:06:00.23,Default,,0000,0000,0000,,vsetko to delene 2 krat A.
Dialogue: 0,0:06:00.23,0:06:02.84,Default,,0000,0000,0000,,Viem, ze to vyzera zlozito, ale cim viacej to budes pouzivat,
Dialogue: 0,0:06:02.84,0:06:04.40,Default,,0000,0000,0000,,uvidis, ze to v skutocnosti nie je az take zle.
Dialogue: 0,0:06:04.40,0:06:07.72,Default,,0000,0000,0000,,Je dobre si ten vzorec zapamatat.
Dialogue: 0,0:06:07.72,0:06:10.73,Default,,0000,0000,0000,,Aplikujme tento vzorec na nasu rovnicu,
Dialogue: 0,0:06:10.73,0:06:12.67,Default,,0000,0000,0000,,ktoru sme si napisali.
Dialogue: 0,0:06:12.67,0:06:15.26,Default,,0000,0000,0000,,Takze - pozri sa, A je iba koeficient
Dialogue: 0,0:06:15.26,0:06:18.61,Default,,0000,0000,0000,,clena x na druhu, ano?
Dialogue: 0,0:06:18.61,0:06:20.30,Default,,0000,0000,0000,,takze A je koeficient clena x na druhú.
Dialogue: 0,0:06:20.30,0:06:23.57,Default,,0000,0000,0000,,B je koeficient clena x. C je konštanta.
Dialogue: 0,0:06:23.57,0:06:25.10,Default,,0000,0000,0000,,Takze aplikujme tento vzorec na nasu rovnicu.
Dialogue: 0,0:06:25.10,0:06:26.25,Default,,0000,0000,0000,,Kolko je B?
Dialogue: 0,0:06:26.25,0:06:28.70,Default,,0000,0000,0000,,B je minus 9.
Dialogue: 0,0:06:28.70,0:06:29.97,Default,,0000,0000,0000,,Mozeme to vidiet tu.
Dialogue: 0,0:06:29.97,0:06:33.98,Default,,0000,0000,0000,,B je minus 9, A je minus 10.
Dialogue: 0,0:06:33.98,0:06:34.97,Default,,0000,0000,0000,,C je 1.
Dialogue: 0,0:06:34.97,0:06:36.09,Default,,0000,0000,0000,,Ano?
Dialogue: 0,0:06:36.09,0:06:42.35,Default,,0000,0000,0000,,Ak B je minus 9 - tak potom mame minus minus 9.
Dialogue: 0,0:06:42.35,0:06:49.26,Default,,0000,0000,0000,,Plus alebo mínus druhá odmocnina minus 9 na druhú.
Dialogue: 0,0:06:49.26,0:06:49.81,Default,,0000,0000,0000,,To je 81.
Dialogue: 0,0:06:49.81,0:06:53.14,Default,,0000,0000,0000,,Mínus 4 krát A.
Dialogue: 0,0:06:56.94,0:06:59.76,Default,,0000,0000,0000,,A je mínus 10.
Dialogue: 0,0:06:59.76,0:07:03.24,Default,,0000,0000,0000,,Mínus 10 krát C, ktore je 1.
Dialogue: 0,0:07:03.24,0:07:05.11,Default,,0000,0000,0000,,Viem, že je to chaoticke, ale dúfam, že to
Dialogue: 0,0:07:05.11,0:07:06.47,Default,,0000,0000,0000,,chapes.
Dialogue: 0,0:07:06.47,0:07:09.56,Default,,0000,0000,0000,,Všetko delene 2 krát A.
Dialogue: 0,0:07:09.56,0:07:14.05,Default,,0000,0000,0000,,A je mínus 10, takze 2 krát A je potom mínus 20.
Dialogue: 0,0:07:14.05,0:07:14.99,Default,,0000,0000,0000,,Tak si to zjednodušme.
Dialogue: 0,0:07:14.99,0:07:19.41,Default,,0000,0000,0000,,minus minus 9, to je kladne 9.
Dialogue: 0,0:07:19.41,0:07:26.46,Default,,0000,0000,0000,,Plus alebo mínus druhá odmocnina z 81.
Dialogue: 0,0:07:26.46,0:07:30.66,Default,,0000,0000,0000,,Máme minus 4 krat A, ktore je minus 10 .
Dialogue: 0,0:07:30.66,0:07:31.87,Default,,0000,0000,0000,,Tu je mínus 10.
Dialogue: 0,0:07:31.87,0:07:33.28,Default,,0000,0000,0000,,Viem, že je to veľmi komplikované, je mi to luto,
Dialogue: 0,0:07:33.28,0:07:34.38,Default,,0000,0000,0000,,krat C, teda krat 1.
Dialogue: 0,0:07:34.38,0:07:39.41,Default,,0000,0000,0000,,minus 4 krat minus 10 je 40, kladne 40.
Dialogue: 0,0:07:39.41,0:07:41.04,Default,,0000,0000,0000,,Kladne 40.
Dialogue: 0,0:07:41.04,0:07:46.07,Default,,0000,0000,0000,,To vsetko vydelime minus 20.\N.
Dialogue: 0,0:07:46.07,0:07:48.30,Default,,0000,0000,0000,,81 plus 40 je 121.
Dialogue: 0,0:07:48.30,0:07:52.33,Default,,0000,0000,0000,,9 plus alebo mínus druhá odmocnina
Dialogue: 0,0:07:52.33,0:07:58.29,Default,,0000,0000,0000,,zo 121 delene mínus 20.
Dialogue: 0,0:07:58.29,0:08:01.62,Default,,0000,0000,0000,,Druhá odmocnina zo 121 je 11.
Dialogue: 0,0:08:01.62,0:08:03.17,Default,,0000,0000,0000,,Pôjdem sem.
Dialogue: 0,0:08:03.17,0:08:06.18,Default,,0000,0000,0000,,Dúfam, že nestratís prehľad o tom, čo robím.
Dialogue: 0,0:08:06.18,0:08:13.72,Default,,0000,0000,0000,,9 plus alebo mínus 11, delene mínus 20.
Dialogue: 0,0:08:13.72,0:08:19.09,Default,,0000,0000,0000,,9 plus 11 delene mínus 20, to je 9
Dialogue: 0,0:08:19.09,0:08:22.54,Default,,0000,0000,0000,,plus 11 je 20, takže to je 20 delene mínus 20,
Dialogue: 0,0:08:22.54,0:08:23.73,Default,,0000,0000,0000,,co sa rovná minus 1 .
Dialogue: 0,0:08:23.73,0:08:24.90,Default,,0000,0000,0000,,Takže tu mame prvy koreň.
Dialogue: 0,0:08:24.90,0:08:28.26,Default,,0000,0000,0000,,To je 9 plus - pretože to je plus alebo mínus.
Dialogue: 0,0:08:28.26,0:08:33.79,Default,,0000,0000,0000,,A ten druhý koreň potom bude 9 mínus 11 delene minus 20,
Dialogue: 0,0:08:33.79,0:08:37.72,Default,,0000,0000,0000,,co sa rovná mínus 2 delene mínus 20,
Dialogue: 0,0:08:37.72,0:08:40.70,Default,,0000,0000,0000,,co sa rovná 1 lomene 10.
Dialogue: 0,0:08:40.70,0:08:42.69,Default,,0000,0000,0000,,Tak toto je dalsi koren.
Dialogue: 0,0:08:42.69,0:08:48.95,Default,,0000,0000,0000,,Ak by sme tuto rovnicu zobrazili na grafe, videli by sme, ze v
Dialogue: 0,0:08:48.95,0:08:52.64,Default,,0000,0000,0000,,bodoch minus 1 a 1/10 naozaj pretína os x.
Dialogue: 0,0:08:52.64,0:08:57.77,Default,,0000,0000,0000,,Alebo f ( x) sa rovna 0 v bodoch, kde x sa rovna
Dialogue: 0,0:08:57.77,0:09:01.69,Default,,0000,0000,0000,,minus 1 alebo x sa rovná 1/10.
Dialogue: 0,0:09:01.69,0:09:04.08,Default,,0000,0000,0000,,V časti 2 budu dalsie príklady, pretože si
Dialogue: 0,0:09:04.08,0:09:06.10,Default,,0000,0000,0000,,myslím, ze ak niečo, tak možno som ta
Dialogue: 0,0:09:06.10,0:09:08.12,Default,,0000,0000,0000,,tymto trocha doplietol.
Dialogue: 0,0:09:08.12,0:09:11.68,Default,,0000,0000,0000,,Uvidíme sa teda v časti 2 s dalsimi
Dialogue: 0,0:09:11.68,0:09:12.15,Default,,0000,0000,0000,,kvadratickymi rovnicami.
Dialogue: 0,0:09:12.15,0:09:14.08,Default,,0000,0000,0000,,...