I-Calculator yeFomula ye-Quadrate
Solve any quadratic equation ax² + bx + c = 0, including complex roots.
Iinketho ze projekti
Malunga nale Calculator
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 ebuza rhoqo
Yintoni ethetha ngayo i-differentiator kum?
I-b² - 4ac echazayo igqiba ngeendawo eziphambili: ezilungileyo zithetha iinkqubo ezimbini ezinyanzelekileyo, i-zero ithetha enye inkqubo ephindaphindwayo, nezingalunganga zithetha iinkqubo ezimbini ezinzima.
Yintoni ukuba i-a yi-zero?
Then the equation is linear, not quadratic, and the quadratic formula does not apply. Enter a non-zero value for a.
Yintoni i vertex yeparabola?
Yindawo yokujika (h, k) apho igophe lifikela khona phezulu okanye ezantsi. Le sixhobo siyixelela kunye nomngxunya ojikelezayo wesimo, umgca x = h.
Ibonisa ntoni ifomu eyenziwe ngezinto ezibini?
Xa iziqwenga ziyinyaniso, uthelekiso lubhalwe kwakhona njenge (x − r₁)(x − r₂). Kuba x² − 5x + 6 = 0 oko kukuthi (x − 3)(x − 2).
Zithini iziqulatho ezinzima?
Xa i-distinct i negative iziqhamo ziyi pair edityaniswe a ± bi ebandakanya iyunithi emiselweyo i i, kwaye isixhobo sibhala ngaphandle kulo hlobo.
Solve x² − 5x + 6 = 0.
I-discriminator yi-1, inika iziqu ezibini ezinyanzelekileyo, x = 3 ne x = 2 — umzekelo ongagqibekanga oboniswe yi-calculator.
API — sebenzisa le calculator ukusuka kwikhowudi
Nceda le khadi lemali njengendawo esemva ye-JSON ekhululekileyo - akukho qhosha lifunekayo. Thumela amaxabiso endawo ezantsi njengeparameter yombuzo okanye i-JSON. Nantoni na oyenzayo isebenzisa okungagqibekanga okufanayo eli phepha ligqityiwe ngaphambili; iparameter engaziwayo yi 400, ayikho i zero ekhululekileyo. Funda i-API epheleleyo →
Incopho yesiphelo
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);Results are estimates for general guidance only, not financial, medical or tax advice.