WEBVTT 00:00:01.010 --> 00:00:04.520 Wamakelekile kwintetho echaza indlela yokusebenzisa i"quadratic equation". 00:00:04.520 --> 00:00:06.730 Ngoko ke i"quadratic equation". ivakala ngathi yinto 00:00:06.730 --> 00:00:07.810 enobunzima kakhulu. 00:00:07.810 --> 00:00:09.930 Kwaye xa uqala ukubona i"quadratic equation, ungathi 00:00:09.930 --> 00:00:11.590 kulungile, hayi ukuphela ivakala njengento 00:00:11.590 --> 00:00:13.110 enobunzima, kodwa yinto enzima. 00:00:13.110 --> 00:00:14.930 Kodwa ngethemba uakubona, njengokuba sisaqubekeka 00:00:14.930 --> 00:00:16.580 nentetho yethu, ukuba ayikhonzima ukuyisebenzisa. 00:00:16.580 --> 00:00:19.040 Kwaye kwintetho ezayo exesheni ndizakubonisa 00:00:19.040 --> 00:00:21.300 indlela eyakhiwe ngayo. 00:00:21.300 --> 00:00:24.810 Ngoko ke, jikelele, sowufundile ukwenza ucalu calulo 00:00:24.810 --> 00:00:25.810 kwiqondo lesibini lalonxaki. 00:00:25.810 --> 00:00:30.910 Ufundile ukuba, ukuba ndino, mandithi "x" ophinda-phindwe kabini thabatha 00:00:30.910 --> 00:00:40.340 "x" thabatha 6, ilingana no0. 00:00:40.340 --> 00:00:42.970 Ukuba bendinalenxaki. "x" ophinda-phindwe kabini thabatha "x" thabtha "x' ilingana 00:00:42.970 --> 00:00:48.720 no0, lanto ungayicalu calulala uthi "x" thabatha 3 kwaye 00:00:48.720 --> 00:00:52.210 "x" dibanisa 2 ilingana no0. 00:00:52.210 --> 00:00:54.955 Ngokucacileyo ithetha ukuba "x" thabatha 3 lingana no 0 okanye 00:00:54.955 --> 00:00:57.073 "x" dibanis 2 lingana no0. 00:00:57.073 --> 00:01:03.512 Ngoko ke "x" thabatha 3 lingana no0 okanye "x' dibanisa 2 lingana no0. 00:01:03.512 --> 00:01:08.500 Ngoko ke "x" lingana no 3 okanye no thabatha 2. 00:01:08.500 --> 00:01:17.980 Kwaye, xa siyizoba phantsi yalento izakuba, ukuba bendino 00:01:17.980 --> 00:01:26.150 msebenzi othile "f" ka "x" ulingana no "x" ophinda-phindwe kabnini thabatha "x' thabatha 6. 00:01:26.150 --> 00:01:28.760 Ngoko ke lomgca usembindini ngoka "f" ka "x". 00:01:28.760 --> 00:01:32.670 Ungaqhelana kakhulu nomgca osembindini we"y". 00:01:32.670 --> 00:01:34.780 kulenxaki inje, akukho nxaki khakhulu. 00:01:34.780 --> 00:01:36.270 Kwaye lomgca usembindini we "x". 00:01:36.270 --> 00:01:40.430 Kwaye ukuba bekuzakufuneka ndiyizobile lenxaki, "x' ophinda-phindwe kabini thabatha "x" 00:01:40.430 --> 00:01:42.380 thabatha 6, ingajongeka ngoluhlobo. 00:01:42.380 --> 00:01:50.130 Kancinci ngoluhlobo--lento ngu "f' ka "x" ulingana no thabatha 6. 00:01:50.130 --> 00:01:52.900 Kwaye umfanekiso ozotyiweyo angakhangeleka ngolu hlobo. 00:01:52.900 --> 00:01:57.150 Nyuka, izakuhlala inyuka ngokwalandlela. 00:02:00.030 --> 00:02:03.150 Kwaye ngoku iya kuthabatha 6, ngoba xa "x' elingana no0. 00:02:03.150 --> 00:02:05.110 'F" ka 'x" ulingana no thabatha 6. 00:02:05.110 --> 00:02:07.800 Ngoko ke ndiyayazi iyagqitha pha kulancam. 00:02:07.800 --> 00:02:11.520 kwaye ndiyayazi ukuba xa "f' ka 'x' elingana no0, ngoko ke 'f' ka 'x' lingana 00:02:11.520 --> 00:02:14.960 no 0 ngaphezu komgca osembindini ka 'x', akunjalo? 00:02:14.960 --> 00:02:16.600 Ngoba lento ngu1. 00:02:16.600 --> 00:02:17.870 lento ngu0. 00:02:17.870 --> 00:02:19.160 lento ngu thabatha 1. 00:02:19.160 --> 00:02:21.510 Ngoko ke lento ngu, xa 'f' ka 'x' elingana no0, ngaphezulu 00:02:21.510 --> 00:02:23.420 komgca osembindini ka 'x', akunjalo? 00:02:23.420 --> 00:02:29.210 Kwaye siyayazi ilingana no0 kula ncam 'x' lingana no 3 kwaye 00:02:29.210 --> 00:02:32.330 'x' lingana no thabatha 2. 00:02:32.330 --> 00:02:34.360 Yeyonanto isiyicombululeyo apha. 00:02:34.360 --> 00:02:36.440 Mhlawumbi xeshikweni besisenza inxaki yokucazulula khange 00:02:36.440 --> 00:02:38.940 siqwalasele ngokomzobo wethu into besiyenza. 00:02:38.940 --> 00:02:42.070 Kodwa ukuba sithi la 'f' ka 'x' ulingana nenaki ethile, sayi 00:02:42.070 --> 00:02:43.270 lungiselela lanto yalingana no0. 00:02:43.270 --> 00:02:44.820 Ngoko ke sithi lenxaki, kuphi apho 00:02:44.820 --> 00:02:48.220 ilingana no0? 00:02:48.220 --> 00:02:49.390 Xa kutheni ilingana no0? 00:02:49.390 --> 00:02:51.720 Kulungile, ilingana no0 kwincam, akunjalo/ 00:02:51.720 --> 00:02:55.360 Ngoba kulapho u'f' ka 'x' elingana no0. 00:02:55.360 --> 00:02:57.490 Kwaye kwangoko into besiyenza xa besisombulula lento ngoku 00:02:57.490 --> 00:03:01.970 cazulula ku, sibonile ukuba, iinxnye zika'x' ezenze u 'f' ka 'x' 00:03:01.970 --> 00:03:04.160 lingana no0, ngokucacileyo ngezi ncam zimbini. 00:03:04.160 --> 00:03:06.740 Kwaye, ngokwe sigama, ezi zibizwa 00:03:06.740 --> 00:03:09.860 ngamaqanda, okanye ingcambu, zika 'f' ka 'x'. 00:03:09.860 --> 00:03:12.470 Makhe siqwalase lanto kancinane. 00:03:14.810 --> 00:03:23.700 Ngoko ke , ukuba ndinento enje ngo'f' ka 'x' ulingana no'x' ophinda-phindwe kabini dibanisa 00:03:23.700 --> 00:03:29.550 '4x' dibanisa 4, kwaye ndibuze kuwe, aphi amaqanda okanye 00:03:29.550 --> 00:03:31.770 ingcambu zika 'f' ka'x'. 00:03:31.770 --> 00:03:33.970 Yinto enye nokuthi, kuphi apho u'f' ka 'x' 00:03:33.970 --> 00:03:36.300 adinana khona nomngca osembindini ka'x'. 00:03:36.300 --> 00:03:38.210 Kwaye badibana xa umgca osembindika ka'x' 'f' ka 'x' eli 00:03:38.210 --> 00:03:39.440 ngana no0, akunjalo? 00:03:39.440 --> 00:03:42.120 Ukuba uyacinga ngomzobo bendikhe ndawenza we'graph'. 00:03:42.120 --> 00:03:45.720 Ngoko ke, masithi ukuba u 'x' ulingana no 0, kwangoko 00:03:45.720 --> 00:03:51.860 singathi, 0 ulingana no'x' ophinda-phindwe kabini dibanisa '4x' dibanisa 4. 00:03:51.860 --> 00:03:53.940 Kwaye siyayazi, singazicalu calula, ngu 'x' 00:03:53.940 --> 00:03:57.080 dibanisa 2 phinda-phinda 'x' dibanisa 2. 00:03:57.080 --> 00:04:07.090 Kwaye siyayazi ukuba iyalingana no0 xa 'x' elingana no thabatha 2. 00:04:07.090 --> 00:04:10.170 'x' ulingana no thabatha 2. 00:04:13.940 --> 00:04:18.270 Kulungile, kancinci--'x' ulingana no thabatha 2. 00:04:18.270 --> 00:04:22.380 Ngoko ke ngoku, siyayazi singamfumana njani u0 xa eyona 00:04:22.380 --> 00:04:24.560 nxaki kulula ukuyicazulula. 00:04:24.560 --> 00:04:27.500 Kodwa masenze eyona nxaki apho inxaki yethu 00:04:27.500 --> 00:04:28.850 kungakho lula ukuyicazulula konke konke. 00:04:28.850 --> 00:04:32.120 Masithi sino 'f' ka 'x' ulingana nothabatha '10x' 00:04:39.750 --> 00:04:45.380 ophinda-phindiweyo kabini thabatha '9x' dibanisa 1. 00:04:45.380 --> 00:04:47.580 Kulungile, xa ndijonga lento, nokuba bendino kuyahlula ngo 10 bendino 00:04:47.580 --> 00:04:48.650 nokufumana amaqhezu apha. 00:04:48.650 --> 00:04:53.130 Kwaye kunzima ukuyicinga indlela yokucazulula lento i'quadratic' 00:04:53.130 --> 00:04:54.860 Kwaye yilonto ibizwa ngokuba yi"quadratic equation" okanye 00:04:54.860 --> 00:04:57.580 liqondo lesibini lamanani anezalathi ezinga phezu kwesithathu. 00:04:57.580 --> 00:04:59.600 Kodwa masiyicwangcise-- Ngoko ke sizama ukuyisombulula lento. 00:04:59.600 --> 00:05:02.420 Ngoba sifuna ukuyazi kuphi xa ilingana no0. 00:05:02.420 --> 00:05:07.130 Thaba '10x' ophonda-phindwe kabini thabatha '9x' dibanisa 1. 00:05:07.130 --> 00:05:09.090 Sifuna ukwazi ngawaphi lamanani asendaweni ka'x' enza lento 00:05:09.090 --> 00:05:11.260 ilingane no0. 00:05:11.260 --> 00:05:13.730 Kwaye apha singasebenzisa isixhobo esibizwa ngokuba yi"quadratic equation". 00:05:13.730 --> 00:05:15.625 Kwaye ngoku ndizakuninika enye kezinqabileyo kwizibalo 00:05:15.625 --> 00:05:18.030 kwaye ngumbono omhle ukuyigcina enqondweni. 00:05:18.030 --> 00:05:21.330 I"quadratic equation' ithi ingcambu ze"quadratic' 00:05:21.330 --> 00:05:24.810 ziyalingana--kwaye masithi i'quadratic equation' ngu 00:05:24.810 --> 00:05:31.900 'x' mophinda-phindwe kabini dibanisa 'bx' dibanisa 'c' lingana no0. 00:05:31.900 --> 00:05:35.790 Ngoko ke kulomzekelo, u'a' ngu thabatha 10. 00:05:35.790 --> 00:05:39.940 'b' ngu thabatha 9, kwaye 'c' ngu 1. 00:05:39.940 --> 00:05:48.040 Isichazi se"quadratic fomula' yi ngcambu ka 'x' ilingana no thabatha 'b' dibanisa okanye thabatha 00:05:48.040 --> 00:05:58.060 ingcambu ephinda-phindwa kabini ka'b' thabatha u 4 phinda-phinda 'a' phinda-phinda 'c', 00:05:58.060 --> 00:06:00.230 yonke lonto ngaphezu ko' 2a'. 00:06:00.230 --> 00:06:02.843 Ndiyayazi ukuba ijongenga nzima kodwa xa uyisebenzisa ngamandla, uzakubona 00:06:02.843 --> 00:06:04.400 ukuba ayikhombi kwaphela. 00:06:04.400 --> 00:06:07.720 Kwaye ngumbono omhle ukuyi bamba ngengqondo. 00:06:07.720 --> 00:06:10.730 Ngoko ke masibandakanye i"quadratic ewauation' apha kulenxaki 00:06:10.730 --> 00:06:12.670 sisandula ukuyibhala phantsi. 00:06:12.670 --> 00:06:15.260 Ngoko ke ndithi sandula ukuthi--kwaye jonga, kukho into ecaleni 00:06:15.260 --> 00:06:18.610 kuka 'x', akunjalo? 00:06:18.610 --> 00:06:20.300 'a' ngumlingani ka 'x' ophinda-phindiweyo. 00:06:20.300 --> 00:06:23.570 'b' ngumlingani ka 'x' kwaye u'c' akatshintshi. 00:06:23.570 --> 00:06:25.100 Ngoko ke masiyisebenzise kule nxaki. 00:06:25.100 --> 00:06:26.250 Ngubani u-'b'? 00:06:26.250 --> 00:06:28.700 Kulungile, 'b' ngu thabatha 9. 00:06:28.700 --> 00:06:29.970 Singabona apha. 00:06:29.970 --> 00:06:33.980 'b' nguthabatha 9, 'a' ngu thabatha 10. 00:06:33.980 --> 00:06:34.970 'c' ngu 1. 00:06:34.970 --> 00:06:36.090 Akunjalo? 00:06:36.090 --> 00:06:42.350 Ngoko ke ukuba u-'b' ngu thabatha 9--ngoko ke masithi, nguthabatha 9. 00:06:42.350 --> 00:06:49.260 Dibanisa okanye thabatha ingcambu kathabatha 9 ophinda-phindwe kabini. 00:06:49.260 --> 00:06:49.810 Kulungile, ngu 81. 00:06:49.810 --> 00:06:53.140 thabatha 4 phinda-phinda ngo 'a' 00:06:56.940 --> 00:06:59.760 'a' ngu thabatha 10. 00:06:59.760 --> 00:07:03.240 Thabatha 10 phinda-phinda 'c', ngokucacileyo ngu 1. 00:07:03.240 --> 00:07:05.110 Ndiyayazi lento ithesa, kodwa ngethemba uza 00:07:05.110 --> 00:07:06.470 kuyiqonda. 00:07:06.470 --> 00:07:09.560 kwaye yonke lonto ngaphezu ko2 umphinda-phinde ngo 'a'. 00:07:09.560 --> 00:07:14.050 Kulungile, 'a' ngu thabatha 10, ngoko ke 2 phinda-phinda 'a' ngu thabahta 20. 00:07:14.050 --> 00:07:14.990 Ngoko ke masiyicazulule lanto. 00:07:14.990 --> 00:07:19.410 Thabatha 10 phinda-phinda ngo thabatha 6, ngu dibanisa 9. 00:07:19.410 --> 00:07:26.460 Dibanisa okanye thabatha ingcambu ka 81. 00:07:26.460 --> 00:07:30.660 Sino thabatha 4 umphinda-phinda ngo thabatha 10. 00:07:30.660 --> 00:07:31.870 Lento ngu thabatha 10. 00:07:31.870 --> 00:07:33.280 Ndiyayazi ithesa kakhulu, ndiyaxolisa kakhulu 00:07:33.280 --> 00:07:34.380 ngalonto, phinda-phinda ngo 1. 00:07:34.380 --> 00:07:39.410 ngoko ke thabatha 4 uphinda-phinde ngo thabatha 10 ngu 40, onesichazi esingu dibanisa 40. 00:07:39.410 --> 00:07:41.040 Dibanisa 40. 00:07:41.040 --> 00:07:46.070 Kwaye kwangoko sinazo zonke phezu ko thabatha 20. 00:07:46.070 --> 00:07:48.300 Kulungile, 81 dibanisa 40 ngu 121. 00:07:48.300 --> 00:07:52.330 Ngoko ke lento ngu 9 dibanisa okanye thabatha ingcambu 00:07:52.330 --> 00:07:58.290 ka 121 phezu ko thabatha 20. 00:07:58.290 --> 00:08:01.620 Ingcambu ka 121 ngu 11. 00:08:01.620 --> 00:08:03.170 Ngoko ke ndizohamba apha. 00:08:03.170 --> 00:08:06.184 Ngethemba awuzose uyiphose indlela yalento ndiyenzayo. 00:08:06.184 --> 00:08:13.720 Ngoko ke lento ngu 9 dibanisa oakanye thabatha 11, ngaphezu ko thabatha 20. 00:08:13.720 --> 00:08:19.090 kwaye ngoko ke ukuba sithi 9 dibanisa 11 phezu ko thabatha 20, ngu 9 00:08:19.090 --> 00:08:22.540 dibanisa 11 ngu 20, ngoko ke lenti ngu 20 phezu ko thabatha 20. 00:08:22.540 --> 00:08:23.730 Ngoku cacileyo ulingana no thabatha 1. 00:08:23.730 --> 00:08:24.900 Ngoko ke yigcambu enye. 00:08:24.900 --> 00:08:28.260 Ngu 9 dibanisa--ngoba lento ngu dibanisa oaknye thabatha. 00:08:28.260 --> 00:08:33.790 Kwaye enye ingcambu izakuba ngu 9 thabatha 11 phezu ko thabatha 20. 00:08:33.790 --> 00:08:37.720 Ngokucacileyo ilingana no thabatha 2 phezu ko thabatha 20. 00:08:37.720 --> 00:08:40.700 ngokucacileyo ilingana no 1 phezu ko 10. 00:08:40.700 --> 00:08:42.690 ngoko ke ngenye ingcambu. 00:08:42.690 --> 00:08:48.950 Ngoko ke ukuba bekunokufuneka ziyizobe phantsi lenxaki, besizokubona ukuba 00:08:48.950 --> 00:08:52.640 ngokucacileyo idibana kumgca osembindini ka'x', 00:08:52.640 --> 00:08:57.770 Okanye 'f' ka 'x' ulingana no0 kwincam ka'x' elingana no thabatha 00:08:57.770 --> 00:09:01.690 1 kwaye 'x' ulingana no 1/10. 00:09:01.690 --> 00:09:04.080 Ndizakwenza imizekelo eminizni kwicandelo lesibini, ngoba ndi 00:09:04.080 --> 00:09:06.100 yacinga, ukuba nantoni na, ndingani bhidekisa 00:09:06.100 --> 00:09:08.120 ngalena yodwa. 00:09:08.120 --> 00:09:11.680 ngoko ke, ndizakunibona kwicandelo lesibini sisebenzisa 00:09:11.680 --> 00:09:12.150 "quadratic equation".