I-Calculator ye-Quadractric Formula
Lungiselela noma iyiphi i-equation ye-quadric ax² + bx + c = 0, kufaka phakathi izimpande ezinzima.
Iziphetho zivuselelwa uma ubhala.
Malunga nale khadi
This calculator solves a quadratic equation ax² + bx + c = 0 using the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. Enter the coefficients a, b and c and it returns both roots, the discriminant, the nature of the roots, the parabola's vertex and axis of symmetry, and the factored form, along with a plot of the curve.
The discriminant b² − 4ac decides everything: a positive value gives two distinct real roots, zero gives one repeated real root, and a negative value gives a pair of complex conjugate roots written with i. Take x² − 5x + 6 = 0 (the defaults, a = 1, b = −5, c = 6): the discriminant is 25 − 24 = 1, so there are two real roots, x = 3 and x = 2, the vertex is at (2.5, −0.25) with axis of symmetry x = 2.5, and the factored form is (x − 3)(x − 2). If a is 0 the equation is linear, not quadratic, and the formula does not apply.
Quadratics model projectile paths, areas, profit-maximizing prices and many optimization problems. The vertex gives the maximum or minimum point of the parabola, while the roots are where it crosses the x-axis.
Imibuzo ebuzwa kaningi
Yini okushoyo umlinganisi?
I-discriminant b² − 4ac ikhetha izimpande: okunengqondo kusho ukuthi amathuluzi amabili angempela, i-zero kusho ukuthi amathuluzi amabili aphindaphindwayo, futhi okubi kusho ukuthi amathuluzi amabili anzima.
Yini uma a iyisizero?
Uma lokhu kwenzeka, i-equation ihamba phambili, ayi-quadric, futhi i-formula ye-quadric ayisebenzi. Faka inani elingekho-zero le-a.
Yini i-vertix ye-parabola?
Yindawo yokushintsha (h, k) lapho i-curve ifinyelela khona okuphezulu noma okuphansi. Le thuluzi liyitshela ngaso kanye ne-axis ye-symmetries, i-line x = h.
Yini okubonisa ifomu elihlukanisiwe?
Uma izimpande ziyiqiniso, inqubekela phambili ibhalwe kabusha njenge (x − r₁)(x − r₂). X² − 5x + 6 = 0 lokho kusho (x − 3)(x − 2).
Yini ama roots anzima?
Uma i-discriminant iyisici esibi, ama roots azoba yi-conjugate pair a ± bi ehlanganisa iyunithi efana ne-i, futhi ithuluzi lizobhala ngazo ngale ndlela.
Thola x2 − 5x + 6 = 0.
I-discriminant yi-1, enikeza izimpande ezimbili ezingokoqobo, x = 3 ne x = 2 — isibonelo esijwayelekile esiboniswa yilesi sinqumo.
API — sebenzisa le calculator kusuka kukhodi
Nquma le calculator njenge JSON evulekile yendawo yokuqeda - akukho isithonjana esidingekayo. Thumela amaxabiso endawo ngezansi njengezilungiselelo zombuzo noma i-JSON. Noma yini ongayishiya isebenzisa iphutha elifanayo elifakwe ngaphambili lekhasi; ipharamitha engaziwa yi-400, ayikho i-zero emnyama. Funda i-API egcwele →
Ingxenye yendawo
GET https://calculator.free/api/v1/quadratic-formula/curl
curl "https://calculator.free/api/v1/quadratic-formula/?a=1&b=-5&c=6"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/quadratic-formula/?" + new URLSearchParams({
"a": "1",
"b": "-5",
"c": "6"
}));
const data = await r.json();
console.log(data.results);Izibalo ziyisilinganiso esisetshenziswa ukuqondisa kuphela, hhayi ukucebisa ngezimali, ukwelashwa noma ukukhokha.