Given a parabola with parametric equations
 |  |  |
(1)
|
 |  |  |
(2)
|
the evolute is given by
 |  |  |
(3)
|
 |  |  |
(4)
|
Eliminating 
and 
gives the implicit equation
 |
(5)
|
With 
,
this can be solved for 
to give
 |
(6)
|
which is known as the semicubical parabola.
From a point above the evolute, three normals can be drawn to the parabola, while only one normal can be drawn to the parabola from a point below the evolute.
