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 root0
Vertex
(-0, 0)
Axis of Symmetry
x = -0
Y-Intercept
(0, 0)
Parabola Graph
Step-by-Step Solution
1. Equation
1x² + 0x + 0 = 0
2. Discriminant
D = b² − 4ac = (0)² − 4(1)(0)
D = 0 − 0 = 0
3. Apply Quadratic Formula
x = (−b ± √D) / 2a
x = (-0 ± √0) / 2
√0 = 0
x₁ = (-0 + 0) / 2 = -0
x₂ = (-0 − 0) / 2 = -0
4. Vertex & Axis of Symmetry
h = −b / 2a = -0 / 2 = -0
k = c − b² / 4a = 0 − 0 / 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
Enter coefficients
Type the values of a, b, and c for the equation ax2 + bx + c = 0.
- 2
Read the roots
The roots x1 and x2 are displayed immediately, along with the discriminant.
- 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?
What is the vertex form?
What if a equals zero?
Is any data sent to a server?
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.