Mpikirakira lasitra
Solve any quadratic equation ax² + bx + c = 0, including complex roots.
Manova ny valin'ny fanoratanao.
Momba ity kapila ity
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.
Fanontaniana matetika
Inona no nolazain'ilay mpanavakavaka amiko?
The discriminant b² − 4ac decides the roots: positive means two real solutions, zero means one repeated solution, and negative means two complex solutions.
Inona no hitranga raha 0 ny a?
Raha izany dia mivadika ho andalana ny famadihana, fa tsy quadrique, ary tsy misy ny fomba fiasan'ny quadratique. Manorata sanda tsy 0 ho an'ny a.
Inona no fototra iorenan'ny parabola?
Io no teboka (h, k) ahitana ny avo indrindra na ny ambany indrindra amin'ilay lokon-drihana. Ity fitaovana ity dia mitatitra izany miaraka amin'ny axe mifamatotra, ny tsipika x = h.
Inona no asehon'ny endrika fanehoana?
Raha tena marina ny fototra, ny fifanakalozana dia voasoratra indray toy ny a (x − r₁)(x − r₂). ho an'ny x² − 5x + 6 = 0 izany hoe (x − 3)(x − 2).
Inona no atao hoe fototra sarotra?
Raha ny soratra dia miseho amin'ny endrika soratra mifono, dia ny soratra dia miseho amin'ny endrika soratra mifono, ary ny soratra dia miseho amin'ny endrika soratra mifono.
Solve x² − 5x + 6 = 0.
Ny 1 no fototra, izay manome ny fototra roa tena izy, x = 3 ary x = 2 — ny ohatra tsy misy ny fototra izay mampiseho ity calculator.
API — mampiasa io milina fanisana io avy amin'ny rindran'asa
Antsoy ho toy ny farany JSON malalaka ity milina fanisana ity - tsy mila famaha. Mandefa ireo sanda eo amin'ny sehatr'asa etsy ambany ho toy ny mpizaratry ny fanontaniana na JSON. Ny zavatra tsy voalaza dia mampiasa ny sanda tsotra efa nameno ity pejy ity; 400 ny sanda tsy fantatra, tsy aotra tsy misy feo. Vakio ny tahirin-kevitra API feno →
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);Ny voka-pikarohana dia natao ho an'ny torohevitra ankapobeny ihany, tsy torohevitra ara-bola, ara-pitsaboana na ara-bola.