Axis of Symmetry Calculator

Find the axis of symmetry and vertex form for parabolas using x = -b/(2a).

Parabola symmetryVertex formStep-by-step solutions

Understanding the axis of symmetry

For parabolas, the axis of symmetry is the vertical line that splits the curve into two mirror halves.

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  • Axis of symmetry formula: For y = ax² + bx + c, the axis is x = -b/(2a).
  • Vertex coordinates: The x-coordinate is -b/(2a), and y is found by substituting this x into the equation.
  • Vertex form: y = a(x - h)² + k reveals vertex (h, k) directly.
  • Parabola direction: If a > 0 the parabola opens up; if a < 0 it opens down.
  • Other conic sections: Ellipses and hyperbolas also have symmetry axes through their center.

How to use this calculator

  1. Select the shape type
  2. Enter coefficients for the equation
  3. Click Calculate
  4. Review axis, vertex, and step-by-step output

Frequently Asked Questions

What is the axis of symmetry?

It is a line that divides a curve into mirrored halves. For y = ax² + bx + c, it is x = -b/(2a).

How do you find the axis of symmetry?

Use x = -b/(2a) from the quadratic coefficients.

What is vertex form?

Vertex form is y = a(x - h)² + k and directly shows the vertex (h, k).

Do ellipses have an axis of symmetry?

Yes. Ellipses have major and minor axes of symmetry.

Can the axis of symmetry be horizontal?

Yes for sideways parabolas (x = ay² + by + c). For y = ax² + bx + c, the axis is vertical.