Izimpande ezothando quadratic: incazelo aljebra weJiyomethri

Ngo-algebra square ibizwa ngokuthi oda ezothando yesibili. Ngu kwesibalo isho isibalo sezibalo, eyabika esikhathini ngezithako zawo elilodwa noma engaziwa kabanzi. Okwesibili-oda equation - ezothando zezibalo kokuba okungenani oyedwa engaziwa ngokwamazinga sikwele. I kwesibalo quadratic - yesibili-oda kwesibalo kuboniswe ungubani ukuze kusho ilingane no-zero. Xazulula isikwele kwesibalo kuyafana ukuthi sithole izimpande skwele ezothando. Ejwayelekile equation Quadratic ifomu jikelele:

W * c ^ 2 T * c + O = 0

lapho W, T - the okuza imisuka ezothando quadratic;

O - Coefficient khulula;

c - empandeni quadratic equation (njalo has amagugu C1 emibili C2).

Njengoba sekushiwo, inkinga ukusombulula equation Quadratic - ekutholeni izimpande ezothando quadratic. Ukuze uthole kubo, udinga ukuthola discriminant:

N = T ^ 2 - 4 * W * O

Amafomula discriminant ezidingekile abawatholi amakhambi impande C1 no C2:

C1 = (-t + √N) / 2 * C2 W futhi = (-t - √N) / 2 * W

Uma equation Quadratic jikelele ifomu factor empandeni T inenani amaningi, ezothando esikhundleni:

W * c ^ 2 + 2 * U * c + O = 0

Futhi izimpande zawo ibukeke inkulumo ethi:

C1 = [-U + √ (U ^ 2-W * O)] / W futhi C2 = [-U - √ (U ^ 2-W * O)] / W

Ngokuvamile kwesibalo ungase ube ukubukeka ukuhluka lapho C_2 bangase bangabi W. Coefficient Kulokhu, ezothando ngenhla has ifomu:

c ^ 2 + F * c + L = 0

lapho F - isici empandeni;

L - khulula isici;

c - impande isikwele (njalo has amagugu C1 emibili C2).

Lolu hlobo lwe-equation ibizwa ngokuthi equation Quadratic inikezwe. Igama elithi "sinciphile" wasuka ifomula actuation ejwayelekile equation Quadratic, uma Coefficient impande W inenani elilodwa. Kulokhu, izimpande equation Quadratic:

C1 = -F / 2 + √ [(F / 2) ^ 2-l)] bese C2 = -F / 2 - √ [(F / 2) ^ 2-l)]

Endabeni amagugu ngisho Coefficient F impande izimpande kuyodingeka isixazululo:

C1 = -F + √ (F ^ 2-l) C2 = -F - √ (F ^ 2-L)

Uma sikhuluma zibalo quadratic, kubalulekile ukukhumbula theorem ka Vieta. Lithi imithetho elandelayo ukuze encishisiwe equation Quadratic:

c ^ 2 + F * c + L = 0

C1 + C2 = -F futhi C1 * C2 = L

Ngokuvamile equation Quadratic equation Quadratic izimpande ukuncika ahlobene:

W * c ^ 2 T * c + O = 0

C1 + C2 = -t / W futhi C1 * C2 = O / W

Manje cabanga ongakhetha of zibalo quadratic futhi izixazululo zabo. Bonke kungaba ezimbili, sengathi ilungu c_2 sishoda ke ezothando ngeke sikwele. Ngakho-ke:

1. W * c ^ 2 T * c = 0 we quadratic equation samuntu ngaphandle factor khulula (ilungu).

Isixazululo:

W * c ^ 2 = -t * c

C1 = 0, C2 = -t / W

2. W * c ^ 2 + O = 0 we quadratic equation samuntu ngaphandle ihlandla lesibili, lapho okufanayo modulo izimpande equation Quadratic.

Isixazululo:

W * c ^ 2 = -O

C1 = √ (-O / W), C2 = - √ (-O / W)

Konke lokhu kwaba Aljibhra. Cabangela incazelo weJiyomethri ephethe equation Quadratic. wesibili oda ezothando ku-geometry esachazwa umsebenzi parabola. kaningi umsebenzi ukuthola izimpande ezothando quadratic ngoba abafundi basesikoleni esiphakeme? Lezi izimpande ukunikeza nomqondo kanjani aphambana umsebenzi igrafu (parabola) ne Ukudidiyela-eksisi - enezingqimba. Uma, kokuba isinqumo ezothando quadratic, sithola isinqumo engenangqondo izimpande, bese empambana ngeke. Uma impande has eyodwa ukubaluleka ngokomzimba, umsebenzi kweqa x-axis endaweni eyodwa. Uma izimpande amabili, khona-ke, ngokulandelana, - amabili amaphuzu ukunquma.

Kuyaphawuleka ukuthi ngaphansi izimpande engenangqondo isho ukubaluleka edangalisayo impande, ngesikhathi ngithola impande. Inani Physical - yiliphi inani emihle noma emibi. Endabeni ekutholeni impande eyodwa kuphela kusho ukuthi izimpande efanayo. Ua ijika e uhlelo Cartesian Ukudidiyela kungabuye oyi-kunqunywa okuza izimpande W noT Uma W inenani HIV, kwamagatsha amabili parabola baqondiswa phezulu. Uma W inenani omubi, - phansi. Futhi, uma Coefficient B has uphawu omuhle, lapho W futhi omuhle, vertex umsebenzi parabola luphakathi "y" kusukela "-" infinity "+" infinity, "c" in the ezahlukene lokususa infinity zero. Uma T - Inani omuhle, futhi W - alivumi, ngakolunye uhlangothi abscissa.