Kodi kupeza pamwamba parabola ndi kum'manganso

Mu masamu, pali lonse mndandanda wa mayina, imene ndi yofunika kulamulidwa ndi aone kuti pali quadratic. kufanana akhoza analemba komanso mosiyana ndi charting pa ntchito nkhwangwa. Mizu ya lalikulu maikwezhoni ndi tigwirizane wa parabola ndi molunjika oh.

General view

The aone kuti pali quadratic ambiri kapangidwe zotsatirazi:

nkhwangwa ² + bx + m'ma = 0

Paudindo "X" ali anawaona ndikuwatenga ngati zosintha osiyana ndi mawu akuti lonse. Mwachitsanzo:

2X ² + 5x-4 = 0;

(× + 7) ² +3 (× + 7) + 2 = 0.

Ngati kumene × wayima monga akuti ndi, m'pofunika kuti aipereke monga variable ndi kupeza mizu ya aone kuti pali lapansi. Pambuyo pake, kuti iwo opotoka a polenomiyo ndi kuthetsa kwa x.

Choncho, ngati (× + 7) = munthu, anthu aone kuti pali akutenga mawonekedwe ² + 3a + 2 = 0.

A = ^{3 2 -4 * 1 * 2 =} 1 ;

ndipo ₁ = (- 3-1) / 2 * 1 = -2;

₂ = (- 3 + 1) / 2 * 1 = -1 .

Pamene mizu ofanana -1 ndi -2 timapeza zotsatirazi:

× + 7 = 2 × + 7 = -1;

× = -9 ndi × = -8.

The mizu ndi mfundo za x-ndondomeko ya mphambano mfundo ndi abscissa wa parabola lapansi. Ndipotu kufunika si wofunika kwambiri pamene cholinga kokha kupeza pamwamba parabola lapansi. Koma akufuna mizu mbali yofunika kwambiri.

Kodi kupeza pamwamba parabola ndi

Tiyeni tibwerere ku aone kuti pali pachiyambi. Kuti tiyankhe funso mmene kupeza pamwamba parabola, ndi kofunika kudziwa mfundo zotsatirazi:

× _SN = -b / 2a,

kumene × _SN - mtengo wa x-ntchito za mfundo ankafuna.

Koma kodi kupeza pamwamba parabola popanda phindu Y-ntchito? Ife mmalo phindu zopezera aone kuti pali × ndi kupeza variable ankafuna. Mwachitsanzo, ife kuthetsa aone kuti pali zotsatirazi:

× ² + 3 = 5 0

Ife kupeza phindu x-ndondomeko za vertex wa parabola ndi:

× _SN = -b / 2a = -3 / 2 * 1;

× _SN = -1,5.

Pezani phindu la Y-ndondomeko za vertex wa parabola ndi:

Y = 2X ² + 4x 3 = (- 1.5) ² +3 * (- 1,5) -5;

Y = -7,25.

Chotsatira kuti parabola pachimake ili pa ndondomeko (-1,5; -7.25).

Ntchito yomanga parabola ndi

parabola ndi pawiri mfundo ndi choimirira olamulira chosokonekera. Pachifukwa ichi, kumanga zake sikovuta. Ovuta kwambiri - ndi kupanga kuwerengetsera olondola a ndondomeko ya mfundo.

Kodi kulabadira makamaka kwa koefishienti wa aone kuti pali quadratic.

The koyefishienti amakhudza malangizo a parabola lapansi. Pankhaniyi pamene ali ndi phindu zoipa, nthambi akuuzidwa kunsi, ndi chizindikiro zabwino - mmwamba.

Koyefishienti b ikusonyeza mmene lonse ndi dzanja parabola. Ikuluikulu mtengo kwambiri, izo zidzakhala.

The koyefishienti limasonyeza kuti kusamutsidwa mu Y-olamulira wachibale chiyambi cha parabola lapansi.

Kodi kupeza pamwamba parabola, ife taphunzira kale, ndi kupeza mizu, ayenera kutsatira ndi mitunduyi zotsatirazi:

D = b ² -4ac,

kumene D - ndi discriminant chimene chili chofunika kupeza mizu ya aone kuti pali lapansi.

× ₁ = ^(- b + V - D) / 2a

× ₂ = ^(- BV - D) / 2a

Mfundo analandira wa × zizigwirizana ndi ziro mfundo za Y, monga Iwo ali tigwirizane ndi x-olamulira.

Kenako tiona pa ndi ntchito ndege la vertex wa parabola ndi mfundo analandira. Kwa ndandanda mwatsatanetsatane kuti tipeze mfundo angapo. Kuti zimenezi zitheke tiyenera kusankha × aliyense mtengo, chovomerezeka ankalamulira, ndipo mmalo mu aone kuti pali ntchito. The chifukwa cha anapezazo ndi ntchito mfundo pa Y-olamulira.

Wosalira ndondomeko ya kumanga ndandanda, mukhoza lembani mzere umodzi mwa vertex wa parabola ndi perpendicular kwa x-olamulira. Ichi chidzakhala olamulira chosokonekera, njira imene, ndi mfundo limodzi, akhoza kumatanthauza ndi equidistant wachiwiri kuchokera mzere kukopedwa.