1
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Wamakelekile kwintetho echaza indlela yokusebenzisa i"quadratic equation".

2
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Ngoko ke i"quadratic equation". ivakala ngathi yinto

3
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enobunzima kakhulu.

4
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Kwaye xa uqala ukubona i"quadratic equation, ungathi

5
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kulungile, hayi ukuphela ivakala njengento

6
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enobunzima, kodwa yinto enzima.

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Kodwa ngethemba uakubona, njengokuba sisaqubekeka

8
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nentetho yethu, ukuba ayikhonzima ukuyisebenzisa.

9
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Kwaye kwintetho ezayo exesheni ndizakubonisa

10
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indlela eyakhiwe ngayo.

11
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Ngoko ke, jikelele, sowufundile ukwenza ucalu calulo

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kwiqondo lesibini lalonxaki.

13
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Ufundile ukuba, ukuba ndino, mandithi "x" ophinda-phindwe kabini thabatha

14
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"x" thabatha 6, ilingana no0.

15
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Ukuba bendinalenxaki. "x" ophinda-phindwe kabini thabatha "x" thabtha "x' ilingana

16
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no0, lanto ungayicalu calulala uthi "x" thabatha 3 kwaye

17
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"x" dibanisa 2 ilingana no0.

18
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Ngokucacileyo ithetha ukuba "x" thabatha 3 lingana no 0 okanye

19
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"x" dibanis 2 lingana no0.

20
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Ngoko ke "x" thabatha 3 lingana no0 okanye "x' dibanisa 2 lingana no0.

21
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Ngoko ke "x" lingana no 3 okanye no thabatha 2.

22
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Kwaye, xa siyizoba phantsi yalento izakuba, ukuba bendino

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msebenzi othile "f" ka "x" ulingana no "x" ophinda-phindwe kabnini thabatha "x' thabatha 6.

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Ngoko ke lomgca usembindini ngoka "f" ka "x".

25
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Ungaqhelana kakhulu nomgca osembindini we"y".

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kulenxaki inje, akukho nxaki khakhulu.

27
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Kwaye lomgca usembindini we "x".

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Kwaye ukuba bekuzakufuneka ndiyizobile lenxaki, "x' ophinda-phindwe kabini thabatha "x"

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thabatha 6, ingajongeka ngoluhlobo.

30
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Kancinci ngoluhlobo--lento ngu "f' ka "x" ulingana no thabatha 6.

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Kwaye umfanekiso ozotyiweyo angakhangeleka ngolu hlobo.

32
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Nyuka, izakuhlala inyuka ngokwalandlela.

33
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Kwaye ngoku iya kuthabatha 6, ngoba xa "x' elingana no0.

34
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'F" ka 'x" ulingana no thabatha 6.

35
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Ngoko ke ndiyayazi iyagqitha pha kulancam.

36
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kwaye ndiyayazi ukuba xa "f' ka 'x' elingana no0, ngoko ke 'f' ka 'x' lingana

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no 0 ngaphezu komgca osembindini ka 'x', akunjalo?

38
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Ngoba lento ngu1.

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lento ngu0.

40
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lento ngu thabatha 1.

41
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Ngoko ke lento ngu, xa 'f' ka 'x' elingana no0, ngaphezulu

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komgca osembindini ka 'x', akunjalo?

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Kwaye siyayazi ilingana no0 kula ncam 'x' lingana no 3 kwaye

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'x' lingana no thabatha 2.

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Yeyonanto isiyicombululeyo apha.

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Mhlawumbi xeshikweni besisenza inxaki yokucazulula khange

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siqwalasele ngokomzobo wethu into besiyenza.

48
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Kodwa ukuba sithi la 'f' ka 'x' ulingana nenaki ethile, sayi

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lungiselela lanto yalingana no0.

50
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Ngoko ke sithi lenxaki, kuphi apho

51
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ilingana no0?

52
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Xa kutheni ilingana no0?

53
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Kulungile, ilingana no0 kwincam, akunjalo/

54
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Ngoba kulapho u'f' ka 'x' elingana no0.

55
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Kwaye kwangoko into besiyenza xa besisombulula lento ngoku

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cazulula ku, sibonile ukuba, iinxnye zika'x' ezenze u 'f' ka 'x'

57
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lingana no0, ngokucacileyo ngezi ncam zimbini.

58
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Kwaye, ngokwe sigama, ezi zibizwa

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ngamaqanda, okanye ingcambu, zika 'f' ka 'x'.

60
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Makhe siqwalase lanto kancinane.

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Ngoko ke , ukuba ndinento enje ngo'f' ka 'x' ulingana no'x' ophinda-phindwe kabini dibanisa

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'4x' dibanisa 4, kwaye ndibuze kuwe, aphi amaqanda okanye

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ingcambu zika 'f' ka'x'.

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Yinto enye nokuthi, kuphi apho u'f' ka 'x'

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adinana khona nomngca osembindini ka'x'.

66
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Kwaye badibana xa umgca osembindika ka'x' 'f' ka 'x' eli

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ngana no0, akunjalo?

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Ukuba uyacinga ngomzobo bendikhe ndawenza we'graph'.

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Ngoko ke, masithi ukuba u 'x' ulingana no 0, kwangoko

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singathi, 0 ulingana no'x' ophinda-phindwe kabini dibanisa '4x' dibanisa 4.

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Kwaye siyayazi, singazicalu calula, ngu 'x'

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dibanisa 2 phinda-phinda 'x' dibanisa 2.

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Kwaye siyayazi ukuba iyalingana no0 xa 'x' elingana no thabatha 2.

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'x' ulingana no thabatha 2.

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Kulungile, kancinci--'x' ulingana no thabatha 2.

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Ngoko ke ngoku, siyayazi singamfumana njani u0 xa eyona

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nxaki kulula ukuyicazulula.

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Kodwa masenze eyona nxaki apho inxaki yethu

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kungakho lula ukuyicazulula konke konke.

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Masithi sino 'f' ka 'x' ulingana nothabatha '10x'

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ophinda-phindiweyo kabini thabatha '9x' dibanisa 1.

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Kulungile, xa ndijonga lento, nokuba bendino kuyahlula ngo 10 bendino

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nokufumana amaqhezu apha.

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Kwaye kunzima ukuyicinga indlela yokucazulula lento i'quadratic'

85
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Kwaye yilonto ibizwa ngokuba yi"quadratic equation" okanye

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liqondo lesibini lamanani anezalathi ezinga phezu kwesithathu.

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Kodwa masiyicwangcise-- Ngoko ke sizama ukuyisombulula lento.

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Ngoba sifuna ukuyazi kuphi xa ilingana no0.

89
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Thaba '10x' ophonda-phindwe kabini thabatha '9x' dibanisa 1.

90
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Sifuna ukwazi ngawaphi lamanani asendaweni ka'x' enza lento

91
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ilingane no0.

92
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Kwaye apha singasebenzisa isixhobo esibizwa ngokuba yi"quadratic equation".

93
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Kwaye ngoku ndizakuninika enye kezinqabileyo kwizibalo

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kwaye ngumbono omhle ukuyigcina enqondweni.

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I"quadratic equation' ithi ingcambu ze"quadratic'

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ziyalingana--kwaye masithi i'quadratic equation' ngu

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'x' mophinda-phindwe kabini dibanisa 'bx' dibanisa 'c' lingana no0.

98
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Ngoko ke kulomzekelo, u'a' ngu thabatha 10.

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'b' ngu thabatha 9, kwaye 'c' ngu 1.

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Isichazi se"quadratic fomula' yi ngcambu ka 'x' ilingana no thabatha 'b' dibanisa okanye thabatha

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ingcambu ephinda-phindwa kabini ka'b' thabatha u 4 phinda-phinda 'a' phinda-phinda 'c',

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yonke lonto ngaphezu ko' 2a'.

103
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Ndiyayazi ukuba ijongenga nzima kodwa xa uyisebenzisa ngamandla, uzakubona

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ukuba ayikhombi kwaphela.

105
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Kwaye ngumbono omhle ukuyi bamba ngengqondo.

106
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Ngoko ke masibandakanye i"quadratic ewauation' apha kulenxaki

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sisandula ukuyibhala phantsi.

108
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Ngoko ke ndithi sandula ukuthi--kwaye jonga, kukho into ecaleni

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kuka 'x', akunjalo?

110
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'a' ngumlingani ka 'x' ophinda-phindiweyo.

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'b' ngumlingani ka 'x' kwaye u'c' akatshintshi.

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Ngoko ke masiyisebenzise kule nxaki.

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Ngubani u-'b'?

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Kulungile, 'b' ngu thabatha 9.

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Singabona apha.

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'b' nguthabatha 9, 'a' ngu thabatha 10.

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'c' ngu 1.

118
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Akunjalo?

119
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Ngoko ke ukuba u-'b' ngu thabatha 9--ngoko ke masithi, nguthabatha 9.

120
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Dibanisa okanye thabatha ingcambu kathabatha 9 ophinda-phindwe kabini.

121
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Kulungile, ngu 81.

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thabatha 4 phinda-phinda ngo 'a'

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'a' ngu thabatha 10.

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Thabatha 10 phinda-phinda 'c', ngokucacileyo ngu 1.

125
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Ndiyayazi lento ithesa, kodwa ngethemba uza

126
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kuyiqonda.

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kwaye yonke lonto ngaphezu ko2 umphinda-phinde ngo 'a'.

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Kulungile, 'a' ngu thabatha 10, ngoko ke 2 phinda-phinda 'a' ngu thabahta 20.

129
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Ngoko ke masiyicazulule lanto.

130
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Thabatha 10 phinda-phinda ngo thabatha 6, ngu dibanisa 9.

131
00:07:19,410 --> 00:07:26,460
Dibanisa okanye thabatha ingcambu ka 81.

132
00:07:26,460 --> 00:07:30,660
Sino thabatha 4 umphinda-phinda ngo thabatha 10.

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Lento ngu thabatha 10.

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00:07:31,870 --> 00:07:33,280
Ndiyayazi ithesa kakhulu, ndiyaxolisa kakhulu

135
00:07:33,280 --> 00:07:34,380
ngalonto, phinda-phinda ngo 1.

136
00:07:34,380 --> 00:07:39,410
ngoko ke thabatha 4 uphinda-phinde ngo thabatha 10 ngu 40, onesichazi esingu dibanisa 40.

137
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Dibanisa 40.

138
00:07:41,040 --> 00:07:46,070
Kwaye kwangoko sinazo zonke phezu ko thabatha 20.

139
00:07:46,070 --> 00:07:48,300
Kulungile, 81 dibanisa 40 ngu 121.

140
00:07:48,300 --> 00:07:52,330
Ngoko ke lento ngu 9 dibanisa okanye thabatha ingcambu

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ka 121 phezu ko thabatha 20.

142
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Ingcambu ka 121 ngu 11.

143
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Ngoko ke ndizohamba apha.

144
00:08:03,170 --> 00:08:06,184
Ngethemba awuzose uyiphose indlela yalento ndiyenzayo.

145
00:08:06,184 --> 00:08:13,720
Ngoko ke lento ngu 9 dibanisa oakanye thabatha 11, ngaphezu ko thabatha 20.

146
00:08:13,720 --> 00:08:19,090
kwaye ngoko ke ukuba sithi 9 dibanisa 11 phezu ko thabatha 20, ngu 9

147
00:08:19,090 --> 00:08:22,540
dibanisa 11 ngu 20, ngoko ke lenti ngu 20 phezu ko thabatha 20.

148
00:08:22,540 --> 00:08:23,730
Ngoku cacileyo ulingana no thabatha 1.

149
00:08:23,730 --> 00:08:24,900
Ngoko ke yigcambu enye.

150
00:08:24,900 --> 00:08:28,260
Ngu 9 dibanisa--ngoba lento ngu dibanisa oaknye thabatha.

151
00:08:28,260 --> 00:08:33,790
Kwaye enye ingcambu izakuba ngu 9 thabatha 11 phezu ko thabatha 20.

152
00:08:33,790 --> 00:08:37,720
Ngokucacileyo ilingana no thabatha 2 phezu ko thabatha 20.

153
00:08:37,720 --> 00:08:40,700
ngokucacileyo ilingana no 1 phezu ko 10.

154
00:08:40,700 --> 00:08:42,690
ngoko ke ngenye ingcambu.

155
00:08:42,690 --> 00:08:48,950
Ngoko ke ukuba bekunokufuneka ziyizobe phantsi lenxaki, besizokubona ukuba

156
00:08:48,950 --> 00:08:52,640
ngokucacileyo idibana kumgca osembindini ka'x',

157
00:08:52,640 --> 00:08:57,770
Okanye 'f' ka 'x' ulingana no0 kwincam ka'x' elingana no thabatha

158
00:08:57,770 --> 00:09:01,690
1 kwaye 'x' ulingana no 1/10.

159
00:09:01,690 --> 00:09:04,080
Ndizakwenza imizekelo eminizni kwicandelo lesibini, ngoba ndi

160
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yacinga, ukuba nantoni na, ndingani bhidekisa

161
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ngalena yodwa.

162
00:09:08,120 --> 00:09:11,680
ngoko ke, ndizakunibona kwicandelo lesibini sisebenzisa

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00:09:11,680 --> 00:09:12,150
"quadratic equation".