Quadratic Equation Calculator
Solve ax² + bx + c = 0 instantly. Shows discriminant, real or complex roots, vertex coordinates, and full step-by-step solution.
ax² + bx + c = 0
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Discriminant (Δ)
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Root Type
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Root x₁
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Root x₂
Vertex and Parabola
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Vertex x
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Vertex y
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Axis of Symmetry
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Opens
Step-by-Step Solution
Extended
Equation Analyzer
Interactive parabola graph, completing the square, and equation properties
Parabola Graph
Graph updates automatically when you change a, b, c above.
Completing the Square — Full Walkthrough
Equation Properties
Professional
Polynomial Solver
Factor form, Vieta's formulas, inequality solver, and table of values
Inequality Solver — When is ax² + bx + c > 0?
Based on your coefficients above. All four inequality forms solved.
Table of Values
Centered around the vertex x = −b/(2a).
Frequently Asked Questions
What is a quadratic equation?
A quadratic equation has the form ax² + bx + c = 0, where a ≠ 0. It can have two real roots, one repeated root, or two complex (imaginary) roots, depending on the discriminant (b² − 4ac).
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) / (2a). The ± means there are generally two solutions (roots). The part under the square root, b² − 4ac, is called the discriminant.
What does the discriminant tell us?
If b² − 4ac > 0: two distinct real roots. If b² − 4ac = 0: one repeated real root. If b² − 4ac < 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. Its x-coordinate is −b/(2a) and the y-coordinate is found by substituting this into the equation. If a > 0, the parabola opens upward; if a < 0, downward.
Why is the quadratic formula important for WAEC and JAMB?
Quadratic equations appear in multiple WAEC Additional Mathematics and JAMB questions every year. Understanding how to derive roots using the formula, completing the square, and factorisation is essential for achieving high scores.