Nzira yekuwana sei vertex yemuenzaniso uye unoivaka

Mune masvomhu kune ruzivo rwakakwana rwezvinyorwa, pakati pazvo nzvimbo inokosha inobatwa ne quadratic equations. Kuenzana kwakadaro kunogona kugadziriswa pamwe chete uye kuronga magrafu pachirongwa chekodzero. Midzi ye quadratic equations ndiwo maonero ekupindirana kwemufananidzo uye mutsara wakarurama wemombe.

General view

Iyo quadratic equation ine chinyorwa chinotevera:

Ax ² + bx + c = 0

Mune basa re "X" rinogona kutaridzirwa semhando dzakasiyana, uye mazwi ose. Somuenzaniso:

2x ² + 5x-4 = 0;

(X + 7) ² + 3 (x + 7) + 2 = 0.

Muchiitiko chacho apo kutaura kunoita basa ra x, zvakakosha kuimiririra sechinoshanduka uye kuwana midzi yean equation. Mushure meizvi, eenzana navo ne polynomial uye ona x.

Saka, kana (x + 7) = a, ipapo kuenzanisa kunotora fomu ² + 3a + 2 = 0.

D = 3 ² -4 * 1 * 2 = 1;

Uye ₁ = (- 3-1) / 2 * 1 = -2;

Uye ₂ = (-3 + 1) / 2 * 1 = -1.

Ne miidzi yakaenzana ne -2 uye -1, tinowana zvinotevera:

X + 7 = -2 uye x + 7 = -1;

X = -9 uye x = -8.

Midzi ndiyo kukosha kwe-x-kuratidzira kwechinhu chekupindirana kwemufananidzo pamwe nekambisi yekambisi. Muchidimbu, kukosha kwavo hakusi kukosha kana basa iri chete kuti riwane vertex yemuenzaniso. Asi pakuronga midzi inobata basa rinokosha.

Nzira yekuwana sei vertex yemuenzaniso

Regai tidzokere kuenzaniso yekutanga. Kuti upindure mubvunzo wekuti ungawana sei vertex yemuenzaniso, zvakakosha kuti uzive rondedzero inotevera:

X mu = -b / 2a,

Ikoko x mune kukosha kwei-kugadzirisa kwepadiwa inoda.

Asi nzira yekuwana sei vertex yemuenzaniso kunze kwey-coordinate value? Isu tinotsiva kukosha kwekuwanikwa kwei x mu equation uye tinowana shanduko inodikanwa. Somuenzaniso, isu tinogadzirisa kuenzanirana kunotevera:

X ² + 3x-5 = 0

Tinowana kukosha kwe x-kuratidzira ye vertex yemuenzaniso:

X mu = -b / 2a = -3 / 2 * 1;

X mu = -1.5.

Tinowana kukosha kwe y-kuronga kwe vertex yemuenzaniso:

Y = 2x2 + 4x-3 = (- 1.5) ² + 3 * (- 1.5) -5;

Y = -7.25.

Somugumisiro, tinowana kuti vertex yemufananidzo inenge yakasvibiswa nehurongwa (-1.5, -7.25).

Kuumba parabola

A parabola isanganidzo yemapurisa ane vertical axis yemakiromita. Nokuda kwechikonzero ichi, kuvaka kwayo iyo haisi yakaoma zvikuru. Chinhu chakanyanya kuoma ndechokuita zviyero zvakakwana zvehutano hwemashoko.

Zvakakodzera kubhadhara zvakananga ku coefficients ye quadratic equation.

Ikoseji inobatanidza chirevo chemufananidzo. Muchiitiko chacho kana ine kukosha kusina kunaka, matavi achaendeswa pasi, uye ane chiratidzo chakanaka.

Ikojiji b inoratidza kuti yakakura sei sleeve yemufananidzo. Iyo yakawanda kukosha kwayo, yakawanda ichava.

Ikojiji c inoratidza kushandiswa kwemafuro emupurisa pamwe chete nheyo yeOY maererano nekwakabva.

Nzira yekuwana nayo vertex yemuenzaniso, tato tadzidza, uye kuti tiwane midzi, munhu anofanirwa kutevera mazita awa anotevera:

D = b ² -4ac,

Ikoko A ari musarudzo anodiwa kuti awane midzi yean equation.

X ₁ = (- b + V ^- D) / 2a

X ₂ = (- bV ^- D) / 2a

Izvo zvakagadziriswa zve x zvichaenderana nezviyero zve zero, kubvira Izvo zvikwangwani zvekubatana-siyana neAxis OX.

Mushure meizvi, tinocherechedza pane imwe ndege yehurumende iyo vertex yemufananidzo uye maitiro akawanikwa. Kuti uwane mamwe mapiritsi akajeka, zvakakosha kuwana dzimwe humwe humwe pfungwa. Kuti tiite izvi, tinosarudza chero kukosha kwei iyo inobvumidzwa nechinzvimbo chetsanangudzo, uye inoiisa iyo kuenzanisa kwebasa racho. Chigumisiro chekuverenga ndeyekubatanidza kwenyaya yacho pamwe neheyi ye OY.

Kuti uite nyore kugadzirisa kuronga, iwe unogona kutora mutsara wakananga kuburikidza ne vertex yechipupuriro uye inopindirana neAxis oX. Iyi ichange iine humwe hutano hwekuenzanisa, iyo iyo, neimwe pfungwa, unogona kuratidza wechipiri, e-equidistant kubva mumutsara.