Skip to content
Kordu Tools

Quadratic Equation Solver

Solve ax2 + bx + c = 0 with real or complex roots, step-by-step solution, vertex, and parabola graph.

1x² + 0x + 0 = 0

x₁

-0

x₂

-0

Discriminant (b² − 4ac)

One repeated real root

0

Vertex

(-0, 0)

Axis of Symmetry

x = -0

Y-Intercept

(0, 0)

Parabola Graph

vertex

Step-by-Step Solution

1. Equation

1x² + 0x + 0 = 0

2. Discriminant

D = b² − 4ac = (0)² − 4(1)(0)

D = 00 = 0

3. Apply Quadratic Formula

x = (−b ± √D) / 2a

x = (-0 ± √0) / 2

0 = 0

x₁ = (-0 + 0) / 2 = -0

x₂ = (-00) / 2 = -0

4. Vertex & Axis of Symmetry

h = −b / 2a = -0 / 2 = -0

k = c − b² / 4a = 00 / 4 = 0

Vertex: (-0, 0) — Axis: x = -0

Vertex form: 1(x − -0)² + 0

Quadratic Formula

x = (−b ± √(b² − 4ac)) / 2a

where a, b, and c are the coefficients of ax² + bx + c = 0.

How to use

  1. 1

    Enter coefficients

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

  2. 2

    Read the roots

    The roots x1 and x2 are displayed immediately, along with the discriminant.

  3. 3

    Explore the details

    Click Show steps for the full working. The parabola graph shows the curve, roots, and vertex.

Frequently asked questions

What if the discriminant is negative?
The equation has two complex roots displayed in a + bi form. The parabola does not cross the x-axis.
What is the vertex form?
The vertex form is a(x - h)2 + k where (h, k) is the vertex. It shows the minimum or maximum point.
What if a equals zero?
The equation is linear (bx + c = 0) with one root: x = -c/b. The solver handles this gracefully.
Is any data sent to a server?
No. All calculations run entirely in your browser.

Enter the coefficients a, b, and c of a quadratic equation and get both

roots instantly, including complex roots when the discriminant is

negative. See the discriminant, vertex, axis of symmetry, y-intercept,

and vertex form. A step-by-step breakdown shows the full quadratic

formula substitution. An SVG parabola graph plots the curve with roots

and vertex labelled. All processing runs in your browser.

Related tools