What is the axis of symmetry?
The vertical line that splits a parabola into mirror-image halves.
Axis of Symmetry Calculator
Compute the line x = −b/(2a) that mirrors a vertical parabola.
Enter quadratic coefficients
Provide a and b from y = ax² + bx + c (a ≠ 0). c is optional for context.
About this calculator
How to use Axis of Symmetry Calculator, plus the formulas and logic behind the results.
Tool description
Every vertical parabola is symmetric about the vertical line through its vertex. That line is x = −b/(2a).
How to use
- Enter a and b (and c if desired).
- Ensure a ≠ 0.
- Select Calculate.
- Read the axis equation and vertex x-coordinate.
Formulas & reference
Axis: x = −b/(2a)Vertex x-coordinate = −b/(2a)
Quick example
- y = x² − 6x + 5 → x = 3
- Vertex lies on the axis
- a controls opening direction
- c shifts the graph vertically
Calculation logic
Divides −b by 2a. Also reports vertex y if c is provided: y = a x² + b x + c.
This applies to vertical parabolas (functions of x).
Axis of Symmetry Calculator FAQ
Common questions about this calculator and how to use the results.
What is the formula?
x = −b/(2a) for y = ax² + bx + c.
Do I need c?
Not for the axis itself; c is used only to report the vertex y-value.
What if a = 0?
Then the graph is not a parabola.
Is the axis always vertical?
For quadratic functions y = ax²+bx+c, yes.
How does this relate to the vertex?
The vertex x-coordinate equals the axis value.