# Quadratic Function: Axis of Symmetry

How to find the axis of symmetry of a quadratic function: formula, 2 examples, and their solutions.

## Formula

The axis of symmetry is the line

that cuts the graph

into two symmetric pieces.

For a quadratic function

y = ax^{2} + bx + c,

the axis of symmetry (green dashed line) is

x = -b/2a.

## Exampley = x^{2} + 4x + 5

Solution

Solution (Detail)

The given quadratic function is

y = 1x^{2} + 4x + 5.

a = 1

b = 4

So the axis of symmetry is

x = -4/[2⋅1].

-4/[2⋅1] = -4/2

-4/2 = -2

So

x = -2

is the answer.

## Exampley = -5x^{2} + x

Solution

Solution (Detail)

The given quadratic function is

y = -5x^{2} + x.

a = -5

b = 1

So the axis of symmetry is

x = -1/[2⋅(-5)].

-1/[2⋅(-5)] = -1/[-10]

-1/[-10] = 1/10

So

x = 1/10

is the answer.