Quadratic Formula Calculator

Type the full equation with =. For inequalities use < > <= >=. For horizontal parabolas use x = ay² + by + c. x^2 + 5x + 6 = 0 · (x-2)(x+3) = 0 · 2(x-3)^2 - 8 = 0 · x^2 - 5x + 6 < 0
Standard: ax^2 + bx + c = 0 — e.g. 2x^2 - 5x + 3 = 0.
Factored: just type the factored form — (x - 2)(x + 3) = 0.
Vertex: a(x - h)^2 + k = 0 — e.g. 2(x - 3)^2 - 8 = 0.
Inequality: use < > <= >= instead of =.
Horizontal parabola: x = ay^2 + by + c with y on the right.
Operators: * for multiplication, / for division, ^ for powers (or x² visually).
ax²+bx+c

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Standard Factored Vertex Inequality Horizontal

or type your own equation above

Solve an equation to see the parabola with vertex, roots, and axis of symmetry.

Quadratic formula x = (−b ± √(b²−4ac)) / 2a
Discriminant Δ = b² − 4ac  (roots: Δ>0 real, =0 repeated, <0 complex)
Vertex x = −b/2a,   y = c − b²/4a

Frequently asked

The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a. It solves any quadratic equation ax² + bx + c = 0. Type the equation into the math field, then click Solve to see every substitution step, the discriminant, and the roots. Handles real, repeated, and complex roots.
The discriminant Δ = b² − 4ac is the expression under the square root in the quadratic formula. Δ > 0: two real roots. Δ = 0: one repeated root. Δ < 0: complex conjugate roots. This calculator computes it automatically and classifies the roots.
Completing the square rewrites ax² + bx + c = 0 as a(x − h)² + k = 0. Steps: divide by a, add (b/2a)² to both sides, factor as a perfect square, then take the square root. Pick Completing the Square from the method dropdown to see every step.
Type the inequality directly — e.g. x^2 - 5x + 6 < 0 — and click Solve. The solver finds roots, uses a sign chart, and writes the answer in interval notation. Example: x² − 5x + 6 < 0 gives x ∈ (2, 3).
Yes — 100% free with no signup. You get 3 solving methods, an interactive Plotly parabola graph, inequality solving with interval notation, LaTeX export, PDF download, image scanning, and shareable URLs. All computation runs in your browser.
Type your equation as ax² + bx + c = 0 in the math field — the calculator extracts a, b, c automatically. Click Solve. You'll see the discriminant, then x = (−b ± √Δ) / 2a with every substitution step. Works for fractions and decimals.
Yes. Type the equation as x = y^2 - 4y + 2 with y on the right. The solver finds the vertex, focus, directrix, and axis of symmetry. You get a step-by-step derivation and an interactive graph of the horizontal parabola.
Click the Practice Worksheet — 1,500+ quadratics with answer key button below the result. The worksheet engine generates printable problem sets across 4 difficulty tiers (basic, medium, hard, scholar) and 26 question types — factoring, quadratic formula, completing the square, discriminant, Vieta's identities, vertex form, NCERT Class 10 word problems (age, speed, rectangle, consecutive integers), parameter problems (real/equal/opposite-sign roots, common root), transformed roots, biquadratic, and JEE Advanced classics (high-power roots via recursion, AM-GM bounds, common-root puzzles). Every problem and answer is CAS-verified.
Yes. Click the 📷 Scan button and upload (or drop in) a photo of a handwritten or printed quadratic equation. The AI vision model extracts the equation, fills the math field automatically, and detects the form (standard, vertex, factored, or inequality). Works on phone snapshots, textbook pages, whiteboard photos, and worksheet scans.
Covers Algebra 1 (factoring, basic quadratic formula), Algebra 2 (discriminant, complex roots, vertex form), Precalculus (parabola conic-section properties, horizontal parabolas), and college algebra. Aligned with Common Core HSA-REI.B.4 and CBSE/ICSE class 9–10 quadratic equations chapter. SAT, ACT, and JEE Mains practice covered.