ToolboxHub

📐Quadratic Equation Solver

Solve quadratic equations (ax² + bx + c = 0) and find roots.

Share:

ax² + bx + c = 0

Root 1 (x₁)

3.000000

Root 2 (x₂)

2.000000

Discriminant

1.00

Vertex

(2.50, -0.25)

Two distinct real roots · Parabola opens upward ↑ · Axis of symmetry: x = 2.50

About Quadratic Equation Solver

Solve any quadratic equation in the form ax² + bx + c = 0 using the quadratic formula. Enter the coefficients a, b, and c to find both roots (real or complex), the discriminant, vertex coordinates, axis of symmetry, and whether the parabola opens up or down. Includes a visual formula breakdown.

How to Use Quadratic Equation Solver

  1. 1

    Enter coefficients

    Type the values for a, b, and c in your equation ax² + bx + c = 0.

  2. 2

    View roots

    Both solutions are displayed instantly along with the discriminant and root type.

  3. 3

    See properties

    View the vertex, axis of symmetry, and direction of the parabola.

Common Use Cases

  • Solving algebra homework and exam problems
  • Finding projectile trajectory intercepts in physics
  • Calculating break-even points in business models
  • Verifying hand-calculated quadratic solutions

Frequently Asked Questions

What is the quadratic formula?
x = (-b ± √(b²-4ac)) / 2a. It gives both solutions of any quadratic equation ax² + bx + c = 0.
What if the discriminant is negative?
If b²-4ac < 0, the equation has two complex (imaginary) roots. The tool displays these in a+bi format.
What does the discriminant tell me?
If discriminant > 0: two distinct real roots. If = 0: one repeated real root. If < 0: two complex conjugate roots.

Related Tools