We vagadzirise quadratic equations uye girafu

Quadratic equations vari equations rechipiri chechetere ane shanduka. Vanoratidza nomufambiro parábola pamusoro ari rinoronga nendege. The aida Midzi dzinomirira pfungwa panguva iyo girafu chinoyambuka X-akabatana. Kubva coefficients inogona pre-kudzidza zvimwe unhu parábola. Somuenzaniso, kana mutengo yakamira pamberi X ² akaipa, asi parábola bazi vachatarira. Uyezve, pane mazano mashomanana kuti ungashandisa kurerutsa mhinduro yacho kupiwa mukana wokuti vanhu vanga.

Mhando quadratic equations

The chikoro akadzidzisa mhando wandei quadratic equations. Zvichienderana mutsauko ichi uye mhinduro. quadratic equations kusiyanisa pakati mhando chaiyo parameter. Izvi mhando ine nhamba variables:

demo ² + 12x 3 = 0

Mumwe kushanduka anogona kutaurwa mukana wokuti vanhu vanga umo shanduka inomiririrwa chete nhamba uye integer okuti:

21 (x + 13) ² -17 (x + 13) -12 = 0

It rakaisirwa zviripo zvose uyu Kazhinji maonero quadratic equations. Dzimwe nguva vanenge akapa mune pamanyorerwo yavanofanira kutanga kuiswa muhurongwa, kuti chinhu kana nyore.

4 (x + 26) ² - (- 43h + 27) (7-x) = 4

Nheyo mumushonga

Quadratic equations zviri kugadziriswa zvinotevera nzira:

1. Kana zvakakodzera, pane imwe nzvimbo zvinogamuchirika tsika.
2. Mukana wokuti vanhu vanga anopiwa nenzira yakakodzera muchimiro.
3. Zvayaiva pamusoro discriminant chaienzanirana nzira: D = b ² -4as.
4. Zvinoenderana kukosha discriminant ndezvipi pamusoro mashandiro. Kana D> 0, ipapo tichiti mukana wokuti vanhu vanga ane midzi mbiri dzakasiyana (pa D).
5. Pashure paizvozvo, kuwana midzi mukana wokuti vanhu vanga.
6. Next (zvichienderana basa) vari vakarangana kana kukosha pane imwe nguva.

Quadratic equations: Theorem Wyeth nemamwe tweaks

Mumwe mudzidzi wekushaiwa kuna vachapenya mukirasi dzavo ruzivo, unyanzvi uye savvy. Panguva mukudzidza quadratic equations zvinogona kuitwa nenzira dzakawanda.

In Kana apo coefficient ane = 1, tinogona kutaura pamusoro pokushandisa Vieta theorem no, maererano iyo Verengai yemidzi akaenzana kukosha b, amire pamberi X (nevakomana chiratidzo raivapo), uye zvinobva X ₁ uye X ₂ akaenzana. equations vakadaro adamwa.

-20h X ² + 91 = 0,

x _{1 *} X ₂ = 91 uye x ₁ + X ₂ = 20 => x = ₁ 13 uye H ₂ = 7

Imwe nzira inofadza kurerutsa mashoko akarongeka oparesheni ndiko kushandisa zvivako zviri parameters. Saka, kana uwandu parameters zvose zviri 0, zvinoreva kuti x ₁ = 1 uye X ₂ = c / a.

17x ² -7h-10 = 0

0 = 07/17/10 saka mudzi 1: x ₁ = 1, uye koren2: x ₂ = -10 / 12

Kana Verengai coefficients uye C akaenzana akundinamata, ipapo x = ₁ uye -1 ukuwo, X ₂ = c / munhu

² + 25x + 24 = 49h 0

25 + 24 = 49 Naizvozvo, _x1 = -1 uye _x2 = -24/25

Kutungamirirwa kugadzirisa quadratic equations nyore zvikuru kuverenga kwacho, uye akaponesa rakawanda nguva. All Zviito chingaitwa mupfungwa, pasina mari inokosha pamusoro kuzvidzora kana rokuongorora basa iri chokuwanziridza muna mbiru kana mashandisirwo karukureta.

Quadratic equations ave kubatana pakati inofananidza uye rinoronga nendege. To nokukurumidza uye nyore kuvaka parábola runoenzanirana basa, zvakakodzera awana pamusoro wayo kudhirowa wehunyambiri mutsetse perpendicular kune x-akabatana. Zvadaro, mumwe pfungwa kunogona kuwanikwa noruremekedzo kuti tinoratidza kupiwa mutsetse, akadana akabatana kuti symmetry.