Quadratic Function: Axis of Symmetry

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

Formula

Formula

The axis of symmetry is the line
that cuts the graph
into two symmetric pieces.

For a quadratic function
y = ax2 + bx + c,

the axis of symmetry (green dashed line) is
x = -b/2a.

Example 1

Example

Solution

The given quadratic function is
y = 1x2 + 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.

Example 2

Example

Solution

The given quadratic function is
y = -5x2 + 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.