What Is an Axis of Symmetry?

An axis of symmetry is a line that divides a shape into two halves. When the shape is folded over this line, the two sides are congruent. For quadratic functions, the axis of symmetry is a vertical line given by a specific formula.

A quadratic function has the standard form equation Ax^2+Bx+C=y. The formula for the axis of symmetry of this function is x=-(B/2A).

This line also goes through a parabola's vertex. To find the y-coordinate of the vertex, substitute the x-coordinate -(b/2a) into the original quadratic equation. For example, if the function is y = x^2-4x+8, then the line of symmetry is -(-4/2)=2=x. To find the vertex, substitute x=2 into the equation to find y=2^2-4(2)+8=4, and the vertex is (2,4).