Quadratic Formula Calculator
Solve quadratic equations ax²+bx+c=0 using the quadratic formula. Find roots, discriminant, and vertex coordinates instantly.
Root x₁
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Root x₂ —
Discriminant (Δ) —
Vertex X —
Vertex Y —
Root Type —
How to Use This Calculator
Enter coefficients a, b, and c for the equation ax²+bx+c=0. The calculator shows both roots (if real), the discriminant, and the vertex of the parabola.
Formula
x = (−b ± √(b²−4ac)) / 2a • Vertex: (−b/2a, f(−b/2a))
Example
x²−5x+6=0: Δ=1 → x=3, x=2 • Vertex at x=2.5, y=−0.25
Frequently Asked Questions
- x = (−b ± √(b²−4ac)) / 2a. It solves any quadratic equation of the form ax²+bx+c=0.
- The discriminant Δ = b²−4ac. If Δ>0 there are two real roots, if Δ=0 one repeated root, if Δ<0 the roots are complex (no real solution).
- The vertex is the minimum or maximum point: x = −b/(2a), y = ax²+bx+c at that x.
- The sign of a determines whether the parabola opens up (a>0, minimum) or down (a<0, maximum). Its magnitude affects how narrow or wide the parabola is.
- No — if a=0 the equation is linear (bx+c=0), not quadratic. The calculator requires a≠0.