The instrument
Three coefficients in; the discriminant, both roots — exact — the vertex and the parabola out. No equals button: the proof writes itself as you type.
How to use it
Sixty seconds to mastery. The solver is live from the first keystroke — here is how to read everything it shows you.
Enter a, b, c
Three boxes, one equation. Type 1, −5, 6 and you're solving x² − 5x + 6 = 0 — the echo line rewrites itself with proper signs as you go.
Watch Δ render its verdict
The discriminant row updates on every keystroke. Its sign tells you the fate of the roots before any formula runs: two real, one double, or a complex pair.
Read the exact roots
The big line never rounds: reduced fractions, simplified surds like −1 ± √2, or a conjugate pair with i. Decimals appear only as a reference row.
Follow the written proof
Under the screen, the full work: substitution into the formula, squares pulled out of the radical, the gcd divided through, Vieta's checks at the end.
Flip to GRAPH
The parabola draws itself around your roots: vertex, axis of symmetry and y-intercept marked, window auto-fitted, complex case flagged honestly.
Learn from the chips
One tap loads a factorable, a surd, a double-root and a complex case — the four personalities of a quadratic. Watch how Δ changes for each.
Questions, answered
The discriminant, the formula, complex roots, Vieta's checks — the quadratic, from every angle.