# What is the axis of symmetry of a parabola? Why do parabolas have them?

##### 1 Answer

Nov 5, 2015

The axis of symmetry of a parabola is the x value of its vertex

#### Explanation:

The axis of symmetry of any function is a line that for any value on one side there is a point opposite it with a point on the axis of symmetry as the midpoint.

graph{x^2 [-10, 10, -5, 5]}

In this graph the axis of symmetry is x=0 for example

An easy way to visualise this is with a butterfly, the body of a butterfly would be its axis of symmetry because the patterns on one side are exactly reflected on the other.