Midzi munhu quadratic mukana wokuti vanhu vanga: algebraic uye geometric zvazvinoreva

In nemasvomhu sikweya anonzi yechipiri hurongwa mukana wokuti vanhu vanga. By mukana wokuti vanhu vanga achireva kwemasvomhu okuti, ine aro Zvinoumba mumwe kana kupfuura kuzivikanwa. Second-kuti mukana wokuti vanhu vanga - munhu akarongeka mukana wokuti vanhu vanga vane dzinenge imwe isingashandiswi pachivara inegumi. The quadratic mukana wokuti vanhu vanga - wechipiri-kuitira mukana wokuti vanhu vanga vakaratidza chitupa kureva akaenzana razero. Vagadzirise mukana wokuti vanhu vanga yaiungana kwakafanana kuti kuona mativi midzi mukana wokuti vanhu vanga. Typical quadratic mukana wokuti vanhu vanga vari mukuru muchimiro:

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

sezvamakaropafadzwa W, T - the coefficients pakati Midzi quadratic mukana wokuti vanhu vanga;

O - free coefficient;

C - Mudzi quadratic mukana wokuti vanhu vanga (nguva dzose ane mbiri tsika C1 uye C2).

Sezvambotaurwa, dambudziko pakugadzirisa quadratic mukana wokuti vanhu vanga - kuwana midzi ane quadratic mukana wokuti vanhu vanga. Kuti tiwane navo, unofanira kuwana discriminant:

N = T ^ 2 - 4 * W * O

The discriminant Masvomhu zvakafanira kuti kuwana mhinduro midzi C1 uye C2:

C1 = (-T + √N) / 2 * W uye C2 = (-T - √N) / 2 * W

Kana quadratic mukana wokuti vanhu vanga ari vakawanda chimiro chakaita pamudzi T ane vakawanda kukosha, mukana wokuti vanhu vanga kuchatsiviwa:

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

Nemidzi yawo Dzakafanana okuti:

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

Kazhinji mukana wokuti vanhu vanga angava siyanei chitarisiko apo C_2 anogona kuva coefficient W. In iyi, pamusoro apa mukana wokuti vanhu vanga ane chimiro:

C ^ 2 + F * C + L = 0

apo F - chinokonzera pamudzi;

L - free chinhu;

C - mudzi pachivara (nguva dzose ane mbiri tsika C1 uye C2).

Izvi rworudzi mukana wokuti vanhu vanga anonzi quadratic mukana wokuti vanhu vanga kupiwa. The zita "ipfupi" akabva payakavakirwa actuation nezvekumwe quadratic mukana wokuti vanhu vanga, kana coefficient pamusoro W mudzi ane ukoshi chete. Panyaya iyi, midzi quadratic mukana wokuti vanhu vanga:

C1 = -F / 2 + √ [(F / 2) ^ 2-L)] uye C2 = -F / 2 - √ [(F / 2) ^ 2-L)]

Kana kunyange tsika pakati coefficient of F mudzi midzi achava mhinduro:

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

Kana isu kutaura quadratic equations, zvinokosha kuyeuka theorem no kuti Vieta. Rinotaura kuti anotevera mitemo kuti wakaderedzwa quadratic mukana wokuti vanhu vanga:

C ^ 2 + F * C + L = 0

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

Vakawanda quadratic mukana wokuti vanhu vanga quadratic mukana wokuti vanhu vanga midzi kufanana dependencies:

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

C1 + C2 = -T / W uye C1 * C2 = O / W

Zvino funga zvokusarudza kuti quadratic equations vavo mhinduro. Vose vanogona kuva maviri, sezvinonzi nhengo c_2 chinoshayikwa, ipapo mukana wokuti vanhu vanga haangavi akaenzana. Naizvozvo:

1. W * C ^ 2 + T * C = 0 ari quadratic mukana wokuti vanhu vanga pachake pasina rusununguko chinhu (nhengo).

The mhinduro iri:

W * C ^ 2 = -T * C

C1 = 0, C2 = -T / W

2. W * C ^ 2 + O = 0 ari quadratic mukana wokuti vanhu vanga pachake pasina rechipiri rokuti, kana zvakafanana modulo Midzi quadratic mukana wokuti vanhu vanga.

The mhinduro iri:

W * C ^ 2 = -O

C1 = √ (-O / W), C2 = - √ (-O / W)

izvi zvose chakanga nemasvomhu. Funga geometric zvinoreva iro rine quadratic mukana wokuti vanhu vanga. wechipiri kuti mukana wokuti vanhu vanga vari geometry kunorondedzerwa imwe parábola chaitika. kazhinji basa iri kuwana midzi munhu quadratic mukana wokuti vanhu vanga kuti vokusekondari? Midzi izvi kupa pfungwa sei piringisha kuti girafu basa (parábola) pamwe rinoronga akabatana - the chinjikira. Kana, wakati akasarudza kuti quadratic mukana wokuti vanhu vanga, tinowana mashoko safunga Mutongo midzi, ipapo mharadzano haazovanzwiri. Kana mudzi ane utano kukosha, mashandiro chinoyambuka x-akabatana panzvimbo imwe. Kana midzi maviri, ipapo, ukuwo, - mbiri dzinokosha mharadzano.

Zvinokosha kucherechedza kuti pasi safunga midzi achireva kunaka ukoshi pasi mudzi, panguva mudzi kuwanikwa. ukoshi panyama - chero zvakanaka kana asina kukosha. Kana yokuwana mudzi mumwe chete kureva kuti midzi zvakafanana. Dzidziso pamusoro munyonga ari Cartesian batanidza maitiro zvinogonawo kwerubwinyo rwakagara rwuripo pakutsvaga coefficients ari W nemidzi uye T. Kana W ane yakanaka kukosha, matavi maviri parábola tinotungamirirwa kumusoro. Kana W ane kunaka kukosha, - pasi. Uyewo, kana coefficient B ane chiratidzo akanaka, sezvamakaropafadzwa W ndiyewo akanaka, iyo vertex ari parábola basa riri mukati 'and "kubva" - "kuti kusaverengeka" + "kusaverengeka," c "iri kuwanda kubvisa kusaverengeka kuti razero. Kana T - zvakanaka kukosha, uye W - akaipa, iri mhiri abscissa.