Question

Why is the vertical line that passes through the vertex of a parabola called the axis of symmetry?

Short answer

The vertical line passing through the vertex of a parabola is called the axis of symmetry because it divides the parabola into two congruent halves, signifying that the parabola is symmetric with respect to this line.

Step-by-step solution

Definition of Parabola

A parabola is a set of all points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix). The vertex of the parabola is the point on the parabola that is closest to the directrix.

Definition of Axis of Symmetry

The axis of symmetry of a parabola is a vertical line that passes through the vertex of the parabola. This line divides the parabola into two congruent halves.

Reason for the Axis of Symmetry

The axis of symmetry is the vertical line that passes through the vertex because, by definition, a parabola is symmetric with respect to this line. This means that if you fold the parabola along this line, the two halves of the parabola will coincide perfectly. Therefore, any point on the parabola has its mirror image on the other side of the axis of symmetry.