Quadratic Equation Calculator

This calculator solves any quadratic equation of the form ax² + bx + c = 0, the standard form you meet in NCEA maths, university papers and problems involving areas, projectile motion or optimisation. You enter the three coefficients, a, b and c, and the tool instantly applies the quadratic formula to find both roots, the x values where the parabola crosses zero. Alongside the roots it works out the discriminant, b squared minus four a c, which shows what kind of solution you have: a positive discriminant gives two distinct real roots, zero gives one repeated root, and a negative discriminant means the roots are complex, shown with the real and imaginary parts. The calculator also returns the vertex of the parabola, the turning point at x equals minus b over two a, useful for sketching the curve or finding a maximum or minimum value. Results update live as you change any coefficient, so you can experiment with different equations and see straight away how the roots, discriminant and vertex shift. Remember that a cannot be zero, because that turns the equation into a straight line rather than a quadratic, and the calculator will flag this if you try it. Whether you are checking homework, studying for an exam or working through a real-world problem that reduces to a quadratic, this tool gives you the full working in seconds.

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