Quadratic Formula Calculator
Kuchotsa iliyonse quadratic kugwirizana ax² + bx + c = 0, kuphatikizapo complex roots.
Zithunzizi zimasintha monga momwe mumalemba.
Zachidule
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.
Mafunso ofunsidwa nthawi zambiri
Kodi kodi discriminant amatiuza ine?
M'mawu ena, mfundo ya 2 ndi 4 ndi mfundo ya 2 ndi 4, ndipo mfundo ya 2 ndi 4 ndi mfundo ya 2 ndi 4.
Kodi ngati a ndi zero?
Ndiyeno kuyerekezera ndi linear, si quadratic, ndi quadratic formula sakugwirizana. Kulowa non-zero tanthauzo kwa a.
Kodi ndi chiyani vertex ya parabola?
Ndipo malo osintha (h, k) komwe mzere umafika pa mlingo wokwanira kapena wotsika. Izi zida zimaziwonetsa limodzi ndi axis ya symmetry, liwiro la x = h.
Kodi factored form amasonyeza chiyani?
Ngati ma roots ndi amodzi, mfundo yofananayo imalembanso ngati a(x − r₁)(x − r₂) chifukwa x² − 5x + 6 = 0, zomwe ndi (x − 3)(x − 2).
Kodi ndi chiyani mbewu zosiyanasiyana?
Ngati mfundo ya 100% ndi yofanana ndi 100%, ndiye kuti mfundoyo ndi yofanana ndi 100% ya mfundo yoyamba, ndipo mfundoyo ndi yofanana ndi 100% ya mfundo yoyamba.
Solve x² − 5x + 6 = 0.
The discriminant ndi 1, kupatsa awiri mbewu zachikhalidwe, x = 3 ndi x = 2 — default chitsanzo anasonyeza ndi izi calculator.
API — kugwiritsa ntchito izi calculator kuchokera code
Kuti mudziwe zambiri, pitani ku www.json.org/json.html. Kuti mudziwe zambiri, pitani ku www.json.org/json.html. Chomweko chilichonse chimene mumasiya chimagwiritsa ntchito mfundo yoyamba yomweyi yomwe tsambali limagwiritsa ntchito; mfundo yosadziwika ndi 400, siyiyenera kukhala zero yosadziwika. Onani zonse API docs →
Chithunzi
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);Zimenezi ndi zowerengera zokhudzana ndi malangizo amtundu uliwonse, si zokhudzana ndi ndalama, zamoyo kapena zokhudzana ndi ndalama.