Quadratic Formula Calculator
Solve chero quadratic equation ax² + bx + c = 0, kusanganisira complex roots.
Zvinyorwa zvinogadziridzwa paunenge uchinyora.
Nezve iyi kalkulator
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.
Zvimwe zvinobvunzwa zvakanyanya
Chii chinonzi discriminant?
Kusiyana b² - 4ac kunopa rusununguko rwekufunga nezvemarudzi ezvinyorwa: Positive zvinoreva kuti pane ma solutions maviri, zero zvinoreva kuti pane imwe soluton, uye negative zvinoreva kuti pane ma soluton maviri.
Chii kana a i zero?
Kana kuti equation iri rakamira, kwete quadratic, uye quadratic formula haisi kutevedzera. Insert a non-zero value for a.
Chii chinonzi vertex yeparabola?
Iyi ndiyo nzvimbo yekuchinja (h, k) iyo kurongeka kunosvika pakukwira kana kukwira. Iyi tool inozivisa ichi pamwe ne axis ye symmetri, iyo line x = h.
Chii chinoratidza fomu yefactored?
Kana rudzi rwemubvunzo rwakanyorwa sea(x − r₁)(x − r₂), ipapo mubvunzo unonyorwa sea(x² − 5x + 6 = 0) kana kuti (x − 3)(x − 2).
Ndezvipi zviuru zvakaoma?
Kana kuti kana kuti kana kuti kana kuti kana kuti kana kuti kana kuti kana kuti kana kuti kana kuti kana kana kuti kana kana kuti kana kana kuti kana kana kuti kana kana kuti kana kana kuti kana kana kuti kana kana kuti kana.
Muenzaniso: 5x + 6 = 0.
The discriminant ndiro 1, kupihwa maviri chokwadi rusununguko, x = 3 uye x = 2 — default muenzaniso akaratidzwa neiyi calculator.
API — kushandisa iyi kalkulator kubva code
Nhare iyi calculator semahara JSON endpoint - hapana chikuru zvinodiwa. Kutumira nzvimbo mavara pasi separameter query kana JSON. Chii zvachose chaunoisa kunze chinoshandisa default iyo peji iri rakasviba nayo; parameter isiri yechokwadi inonzi 400, uye haisi zero. Tora yakazara API docs →
Endpoint
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);Zviratidzo zvemubvunzo ndezvekufungidzira kwechinangwa chekudzidzisa chete, kwete zvemari, zvehutano kana zvemari.