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 = ax2 + bx + c,
the axis of symmetry (green dashed line) is
x = -b/2a.
Exampley = x2 + 4x + 5
Solution
Solution (Detail)
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.
Exampley = -5x2 + x
Solution
Solution (Detail)
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.