I Tavi
I Tavi I Tavi
56 I TavSi Seswavlili masalis mokle mimoxilva ● f : x →x 2 funqciis grafiks parabola ewodeba . f : x →x 2 funqciis Tvisebebi parabolis Tvisebebi 1. y = x 2 funqciis mniSvnelobebi arauaryofiTia. 2. x-is nebismieri mniSvnelo bisa Tvis sruldeba: f(x) = f(–x). 3. funqciis umciresi mniSvnelo baa 0. f(0)=0. m0 A=∅ A={0} A={ ; − } 1. parabola moTavsebulia x-Rer Zis zeda naxevarsibrtyeSi. 2. simetriulia y-RerZis mimarT. 3. M(0,0) wertili parabolis `uR rme si~ wertilia. mas parabo lis wvero ewodeba. ax 2 +bx+c=0 kvadratuli gantoleba sruli arasruli ax 2 +bx=0 ax 2 +c=0 ax 2 =0 ax 2 +bx+c=0 saxis gantolebas, sadac a,b,c∈R, a≠0, xolo x ucnobia, kvadratuli gantoleba ewodeba. b2 – 4ac gamosaxulebas diskriminanti ewodeba – D = b2 – 4ac. ax 2 +bx+c=0, a≠0 kvadratul gantolebas Tu: b b ac a) D>0, aqvs ori gansxvavebuli amonaxseni: x = a − ± − 2 4 . 2 b) D=0 _ erTi amonaxseni: x = – b 2a (ori erTmaneTis toli amonaxseni). g) D
- 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 46 and 47: I Tavi 44 yuradReba: Tu D=0, maSin,
- 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
56<br />
I TavSi Seswavlili masalis mokle mimoxilva<br />
● f : x →x 2 funqciis grafiks parabola ewodeba .<br />
f : x →x 2 funqciis Tvisebebi parabolis Tvisebebi<br />
1. y = x 2 funqciis mniSvnelobebi arauaryofiTia.<br />
2. x-is nebismieri mniSvnelo bisa Tvis<br />
sruldeba: f(x) = f(–x).<br />
3. funqciis umciresi mniSvnelo baa 0.<br />
f(0)=0.<br />
m0<br />
A=∅ A={0} A={ ; − }<br />
1. parabola moTavsebulia x-Rer Zis zeda<br />
naxevarsibrtyeSi.<br />
2. simetriulia y-RerZis mimarT.<br />
3. M(0,0) wertili parabolis `uR rme si~<br />
wertilia. mas parabo lis wvero ewodeba.<br />
ax 2 +bx+c=0<br />
kvadratuli gantoleba<br />
sruli<br />
arasruli<br />
ax 2 +bx=0 ax 2 +c=0 ax 2 =0<br />
ax 2 +bx+c=0 saxis gantolebas, sadac a,b,c∈R, a≠0, xolo x ucnobia, kvadratuli gantoleba<br />
ewodeba.<br />
b2 – 4ac gamosaxulebas diskriminanti ewodeba – D = b2 – 4ac.<br />
ax 2 +bx+c=0, a≠0 kvadratul gantolebas Tu:<br />
b b ac<br />
a) D>0, aqvs ori gansxvavebuli amonaxseni: x =<br />
a<br />
− ± −<br />
2<br />
4<br />
.<br />
2<br />
b) D=0 _ erTi amonaxseni: x = – b<br />
2a<br />
(ori erTmaneTis toli amonaxseni).<br />
g) D
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