Quadratic Formula Calculator

How to use

1. 1Enter the three coefficients a, b, and c from your equation a x^2 + b x + c = 0. a cannot be zero, otherwise the equation is not quadratic.
2. 2Read the discriminant D = b^2 - 4ac at the top of the Result panel and the classification: two distinct real, one repeated, or two complex conjugate roots.
3. 3Copy the individual roots, the vertex (h, k), the axis of symmetry, the y-intercept, the factored form, or the integer factorization if it exists, with the Copy buttons next to each card.
4. 4Look at the parabola preview to confirm the shape, the roots where the curve crosses the x-axis, and the location of the vertex and y-intercept.
5. 5Open the step-by-step derivation to copy the working into a homework write-up or a code review. Tap any preset to load a textbook example.
6. 6Pick a decimal-places setting in the top-right to control how irrational roots and the vertex are rounded in the display.

About this tool

Quadratic Formula Calculator solves any equation of the form a x^2 + b x + c = 0 in your browser and shows the full analytic picture a student or engineer expects to see. Enter the three coefficients (integers, decimals, comma-decimals, or simple fractions like 3/4), and the tool returns the discriminant D = b^2 - 4ac, classifies the roots (two distinct real, one repeated real, or two complex conjugate), and computes them with the quadratic formula x = (-b plus or minus the square root of b^2 - 4ac) divided by 2a. When the discriminant is negative the roots are displayed in p plus or minus q i form with the real and imaginary parts split out so they read clearly. Alongside the roots you get the vertex (h, k) where h = -b/(2a) and k = c - b^2/(4a), the axis of symmetry x = h, the y-intercept (0, c), the direction the parabola opens (up when a is positive, down when a is negative), the sum of roots -b/a, and the product of roots c/a from Vieta's formulas. When the roots are real the tool prints the factored form a(x - r1)(x - r2), and when the coefficients are integers and the roots are rational it also prints an integer factorization like (2x - 1)(x + 2) = 0 by searching divisor pairs of a and c. A step-by-step derivation lists every line a teacher expects in a homework write-up: identify the coefficients, write the formula, substitute the values, compute the discriminant, and read off the roots. An SVG parabola preview centered on the vertex marks the real roots, the vertex, the axis of symmetry, and the y-intercept, so the geometric picture sits next to the algebra. Built-in presets cover the canonical cases that appear on every algebra worksheet: two distinct real roots, a perfect square trinomial with a repeated root, a negative discriminant with complex roots, a leading coefficient other than 1, irrational roots involving square roots of 2, and fractional coefficients. Useful for algebra 1 and algebra 2 homework, pre-calculus and physics problem sets (projectile motion, free-fall time, intersections of conic sections), trigonometry identities that reduce to a quadratic in sine or cosine, statistics regressions, engineering and economics break-even analysis, and quick sanity checks before plugging the answer into a graphing calculator. Coefficients and computed values stay in your browser.

Free to use. Works in your browser. No signup, no login.