I Tavi
I Tavi I Tavi
I Tavi 44 yuradReba: Tu D=0, maSin, rogorc cnobilia, x 1 =x 2 , amitom ax 2 +bx+c=a(x–x 1 ) 2 Tu D
savarjiSoebi: 1 SesaZlebelia Tu ara, rom sxvadasxva kvadratul samwevrs hqondes erTi da igive fesvebi? 2 SesaZlebelia Tu ara, rom sxvadasxva kvadratul funqciebs hqondeT erTi da igive nulebi? dadebiTi pasuxis SemTxvevaSi aCveneT, ra aqvT saerTo da riT gansxvavdebian maTi grafikebi erTmaneTisgan. 3 rogor iqnebian ganlagebulni erTmaneTis mimarT kvadratul funqciaTa grafikebi, romelTa a) fesvebis jami erTmaneTis tolia; b) fesvebis namravli erTmaneTis tolia. 4 ipoveT kvadratuli samwevris fesvebi: a) x 2 –8x+15; b) y 2 –7y+6; g) x 2 +15x+56; d) 0,3x 2 +1,5x–0,9; e) 0,2m 2 +3m–20; v) 3x 2 –3x+1. 5 SeamowmeT, aqvs Tu ara kvadratul samwevrs fesvebi. dadebiTi pasuxis SemTxvevaSi ipoveT maTi jami da namravli: a) 3x 2 –2x–5; b) 2t 2 –t+5; g) 3,4x 2 –14x+1; d) 5m 2 –12m+2; e) 5m 2 –12m–2; v) 0,3x 2 –2x–1. 6 kvadratuli samwevri daSaleT mamravlebad: a) x2 –2x–15; b) x2 –5x–14; g) x2 –x–20; d) 2x2 –x–3; e) 8t2 –6t+1; v) 25t2 –20t+4; z) 4z2 –12z+9; T) –7x2 +22x–3; i) –2x2 +5x+7; k) –35x2 +19x–2; l) –3x2 +38x–120; m) –3x2 +6x+9; n) x2 – 3 1 x+ 4 8 ; o) x2 +2x+ 3 ; 4 1 p) 4 a2 –2a+4; J) – 2 3 a2 –4a–6. 7 SekveceT wiladi: a) x2 –5x+6 x2 +4x–12 ; b) d) 2t2 –6t–8 –3t2 –4t–1 ; e) 7m2 +m–8 7m–7 x2 –16 x2 –x–12 8 amoxseniT gantoleba: a) x2 +7x+10 x2 –x–6 =0; b) g) 13 2x2 +x–21 + 1 2x+7 = 6 x2 ; –9 d) ; g) ; v) 2x 2 –3x–2 a+110–a 2 a2 –22–9a 2x2 –3x–2 8x2 –2 6x 2 +5x+1 =0; 3 x+2 + 2x–1 x+1 = 9 ageT y = x2 –2x–8 da y = x + 2 funqciaTa grafikebi. x–4 riT gansxvavdeba es grafikebi erTmaneTisagan? ; . 2x–1 x 2 +3x+2 . 45
- Page 3: nana jafariZe maia wilosani nani
- Page 6 and 7: IV Tavi . . . . . . . . . . . . . .
- Page 8 and 9: 6 rogor visargebloT wigniT wignze m
- Page 10 and 11: I Tavi 8 f funqciaa h ar aris funqc
- Page 12 and 13: I Tavi gasaxseneblad! p(A) = m n ,
- Page 14 and 15: I Tavi -4 12 4 a) savarjiSoebi: 1 r
- Page 16 and 17: I Tavi 14 4) rodis moawyves turiste
- Page 18 and 19: I Tavi 16 2 amovicnoT wrfivi funqci
- Page 20 and 21: I Tavi 18 SeavseT gamotovebuli adgi
- Page 22 and 23: I Tavi 20 proeqti: gazomvebidan fun
- Page 24 and 25: I Tavi 22 y 10 -3 -2 -1 0 1 2 3 9 8
- Page 26 and 27: I Tavi 24 15% 1,5 < n ≤ 2 20% 1 <
- Page 28 and 29: I Tavi 26 nax. 1 kvadratul gantoleb
- Page 30 and 31: I Tavi 28 3 dawereT kvadratuli gant
- Page 32 and 33: I Tavi davazustoT! roca D = 0, kvad
- Page 34 and 35: I Tavi 32 amovxsnaT formuliT (3x 2
- Page 36 and 37: I Tavi 34 z) 10x 2 −120 + 6x = 98
- Page 38 and 39: I Tavi navis sakuTari siCqarea navi
- Page 40 and 41: I Tavi 38 6 amovxsnaT jgufuri mecad
- Page 42 and 43: I Tavi x 1 da x 2 ricxvebi arian x
- Page 44 and 45: I Tavi 42 17 amoxseniT gantoleba: a
- Page 48 and 49: I Tavi gavixsenoT! x = a, maSin a 2
- Page 50 and 51: I Tavi 48 I Tavis damatebiTi savarj
- Page 52 and 53: I Tavi 50 K y = x 2 A B -3 -2 -1 K
- Page 54 and 55: I Tavi 52 39 A punqtidan B punqtisa
- Page 56 and 57: I Tavi narevSi gaxsnili nivTierebis
- Page 58: 56 I TavSi Seswavlili masalis mokle
savarjiSoebi:<br />
1 SesaZlebelia Tu ara, rom sxvadasxva kvadratul samwevrs<br />
hqondes erTi da igive fesvebi?<br />
2 SesaZlebelia Tu ara, rom sxvadasxva kvadratul funqciebs<br />
hqondeT erTi da igive nulebi? dadebiTi pasuxis SemTxvevaSi<br />
aCveneT, ra aqvT saerTo da riT gansxvavdebian maTi grafikebi<br />
erTmaneTisgan.<br />
3 rogor iqnebian ganlagebulni erTmaneTis mimarT kvadratul<br />
funqciaTa grafikebi, romelTa<br />
a) fesvebis jami erTmaneTis tolia;<br />
b) fesvebis namravli erTmaneTis tolia.<br />
4 ipoveT kvadratuli samwevris fesvebi:<br />
a) x 2 –8x+15; b) y 2 –7y+6; g) x 2 +15x+56;<br />
d) 0,3x 2 +1,5x–0,9; e) 0,2m 2 +3m–20; v) 3x 2 –3x+1.<br />
5 SeamowmeT, aqvs Tu ara kvadratul samwevrs fesvebi. dadebiTi<br />
pasuxis SemTxvevaSi ipoveT maTi jami da namravli:<br />
a) 3x 2 –2x–5; b) 2t 2 –t+5; g) 3,4x 2 –14x+1;<br />
d) 5m 2 –12m+2; e) 5m 2 –12m–2; v) 0,3x 2 –2x–1.<br />
6 kvadratuli samwevri daSaleT mamravlebad:<br />
a) x2 –2x–15; b) x2 –5x–14; g) x2 –x–20; d) 2x2 –x–3;<br />
e) 8t2 –6t+1; v) 25t2 –20t+4; z) 4z2 –12z+9; T) –7x2 +22x–3;<br />
i) –2x2 +5x+7; k) –35x2 +19x–2; l) –3x2 +38x–120; m) –3x2 +6x+9;<br />
n) x2 – 3 1<br />
x+<br />
4 8 ; o) x2 +2x+ 3<br />
;<br />
4<br />
1<br />
p)<br />
4 a2 –2a+4; J) – 2<br />
3 a2 –4a–6.<br />
7 SekveceT wiladi:<br />
a)<br />
x2 –5x+6<br />
x2 +4x–12<br />
; b)<br />
d)<br />
2t2 –6t–8<br />
–3t2 –4t–1<br />
; e)<br />
7m2 +m–8<br />
7m–7<br />
x2 –16<br />
x2 –x–12<br />
8 amoxseniT gantoleba:<br />
a)<br />
x2 +7x+10<br />
x2 –x–6<br />
=0; b)<br />
g)<br />
13<br />
2x2 +x–21 +<br />
1<br />
2x+7 =<br />
6<br />
x2 ;<br />
–9<br />
d)<br />
; g)<br />
; v)<br />
2x 2 –3x–2<br />
a+110–a 2<br />
a2 –22–9a<br />
2x2 –3x–2<br />
8x2 –2<br />
6x 2 +5x+1 =0;<br />
3<br />
x+2<br />
+ 2x–1<br />
x+1 =<br />
9 ageT y = x2 –2x–8<br />
da y = x + 2 funqciaTa grafikebi.<br />
x–4<br />
riT gansxvavdeba es grafikebi erTmaneTisagan?<br />
;<br />
.<br />
2x–1<br />
x 2 +3x+2 .<br />
45
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