What is the quadratic formula?

The quadratic formula x = (-b ± √(b²-4ac)) / 2a solves any equation of the form ax² + bx + c = 0. It was known to ancient Babylonians and is one of the most important formulas in algebra.

What does the discriminant tell us?

If Δ > 0: two distinct real roots. If Δ = 0: one repeated real root. If Δ < 0: two complex conjugate roots (no real solutions).

What is the vertex of a parabola?

The vertex is the highest or lowest point of the parabola y = ax² + bx + c. It occurs at x = -b/(2a). If a > 0, the vertex is a minimum; if a < 0, it is a maximum.

Can I solve cubic or higher-degree equations here?

This calculator is specifically for quadratic (degree 2) equations. Higher-degree polynomials require different methods.

What is the quadratic formula?

The quadratic formula x = (-b ± √(b²-4ac)) / 2a solves any equation of the form ax² + bx + c = 0. It was known to ancient Babylonians and is one of the most important formulas in algebra.

What does the discriminant tell us?

If Δ > 0: two distinct real roots. If Δ = 0: one repeated real root. If Δ < 0: two complex conjugate roots (no real solutions).

What is the vertex of a parabola?

The vertex is the highest or lowest point of the parabola y = ax² + bx + c. It occurs at x = -b/(2a). If a > 0, the vertex is a minimum; if a < 0, it is a maximum.

Can I solve cubic or higher-degree equations here?

This calculator is specifically for quadratic (degree 2) equations. Higher-degree polynomials require different methods.

Educational Tool — Estimates for educational purposes only. Not financial advice.Disclaimer

The quadratic equation is one of the most fundamental concepts in algebra. This calculator solves any equation of the form ax² + bx + c = 0, showing the discriminant, roots (real or complex), vertex, and axis of symmetry.

Quadratic Equation Calculator

Solve quadratic equations (ax² + bx + c = 0) and find real or complex roots using the quadratic formula.

January 2026

Coefficient a (x²)

Must not be zero

Coefficient b (x)

Coefficient c (constant)

Your Results

Discriminant (Δ)

Root x₁

Root x₂

Vertex x

2.5

Vertex y

-0.25

Root Type

Two distinct real roots

Wally's Analysis

AI-powered interpretation of your results

AI Summary

Key Insights

Optimization

What-If Scenarios

AI Disclosure

Wally's Analysis uses GPT-4o-mini for educational interpretations. AI responses are not personalized financial advice and may be inaccurate. All core calculations are deterministic — AI only interprets results.AI Transparency →

Accuracy Commitment

Industry-standard formulas vetted against IRS, SSA, BLS, CFPB. Client-side calculations. Regularly updated.

This calculator provides mathematical results for educational purposes. Always verify critical calculations independently.

Updated: January 2026 · Methodology

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