I Tavi
I Tavi
I Tavi
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4 kvadratuli<br />
gantolebis grafikuli<br />
amoxsna<br />
1. kvadratuli formis yvavilnars 1m siganis zoli<br />
miuerTes. miRebuli nakveTis farTobi 6 m 2 -ia.<br />
ipoveT Tavdapirveli nakveTis gverdis sigrZe.<br />
amoxsna:<br />
vTqvaT, Tavdapirveli nakveTis gverdis sigrZe x m<br />
iyo, maSin miRebuli marTkuTxa nakveTis farTobi<br />
iqneba x(x+1). miviReT gantoleba:<br />
x(x + 1) = 6<br />
x 2 + x – 6 = 0<br />
miRebul gantolebas kvadratul gantolebas uwodeben.<br />
ax 2 +bx+c=0 saxis gantolebas, sadac a,b,c∈R, a≠0, xolo x<br />
ucnobia, kvadratuli gantoleba ewodeba .<br />
a-s kvadratuli gantolebis pirvel koeficients uwodeben,<br />
b-s _ meore koeficients, xolo c-s _ mesame koeficients<br />
(<strong>Tavi</strong>sufal wevrs).<br />
amovxsnaT grafikulad ax 2 + bx + c = 0, a ≠ 0 (1) gantoleba.<br />
I. (1) gantolebas mivceT x2 = kx + m saxe.<br />
(ax2 + bx + c = 0) ⇔ |:a<br />
(x2 + b c<br />
x +<br />
a a = 0) ⇔ (x2 = – b c<br />
x –<br />
a a )<br />
Tu – b c<br />
≡ k da – ≡ m,<br />
a a<br />
maSin miviRebT x2 = kx + m.<br />
II. erTsa da imave marTkuTxa<br />
sakoordinato sistemaSi avagoT<br />
y = x 2 da y = kx + m funqciaTa<br />
grafikebi.<br />
magaliTad,<br />
x 2 = _0,5x + 1,5<br />
(x 2 = –0,5x +1,5) ⇔<br />
x = –1,5<br />
x =1<br />
III. grafikebis gadakveTis<br />
wertilTa abscisebi iqneba (1)<br />
gantolebis amonaxsnebi.<br />
ramdeni saerTo wertili<br />
SesaZlebelia hqondes<br />
wrfesa da parabolas?<br />
parabolas wrfesTan<br />
SesaZlebelia hqondes:<br />
I. ori saerTo<br />
wertili<br />
II. erTi saerTo<br />
wertili<br />
III. arc erTi saerTo<br />
wertili<br />
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