Quadratic Formula Calculator
Los enige kwadmatiese vergelyking byx2 + bx + c = 0 op, insluitende komplekse wortels.
Resultate werk op soos jy tik.
Aangaande hierdie sakrekenaar
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.
Dikwels gevra vrae
Wat sê die teenstrydigheid vir my?
The discriminant b² − 4ac decides the roots: positive means two real solutions, zero means one repeated solution, and negative means two complex solutions.
Sê nou'n is nul?
Dan is die vergelyking lineêre, nie kwadrupmatiese, en die kwadmatiese formule is nie van toepassing. Invoer 'n non-nul waarde vir' n.
Wat is die vetkop van die parabola?
Dit is die keerpunt (h, k) waar die kurwe sy maksimum of minimum bereik. Hierdie nutsprogram berig dit tesame met die as van simmetrie, die lyn x = h.
Wat toon die faktorvorm?
When the roots are real, the equation is rewritten as a(x − r₁)(x − r₂). For x² − 5x + 6 = 0 that is (x − 3)(x − 2).
Wat is komplekse wortels?
Wanneer die diskriminant negatief is, is die wortels 'n konjugasie paar' n ☞ bi waarby die denkbeeldige eenheid i betrokke is, en die gereedskap skryf dit in daardie vorm uit.
Solve x² − 5x + 6 = 0.
Die diskriminant is 1, wat twee ware wortels gee, x = 3 en x = 2 takies met die verstekvoorbeeld wat deur hierdie sakrekenaar vertoon word.
API ← gebruik hierdie sakrekenaar van kode
Bel hierdie sakrekenaar as 'n vry JSON-punt takies wat nodig is. Stuur die veldwaardes hieronder as navraag parameters of JSON. Enigiets wat jy weglaat gebruik dieselfde verstek hierdie bladsy is vooraf gevul met; 'n onbekende parameter is 'n 400, nooit' n stil nul. Lees die volle API docs →
Einde punt:
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);Die resultate is skattings van algemene leiding, nie net finansiële, mediese of belastingvoorligting nie.