Click on the blue point and drag it to change the figure.
Note that the blue point on the line of symmetry is always the same distance from the sides of the parabola.
 Manipulative 1  Line of Symmetry of a Parabola Created with GeoGebra. 

A line of symmetry is a
line
about which a geometric object or objects are reflection symmetrical.
Manipulative 1 shows the line of symmetry of a parabola. If the parabola
is reflected about this line of symmetry it remains unchanged.
A function
may have an
inverse.
A function and its inverse are symmetrical around the line y = x.
Manipulative 2 shows the function y = x^{2}/4 and its inverse,
y = (4x)^{1/3}. Click on the light blue point labeled
'ClickNDrag' and drag it along the line y = x. Note that the
line is equidistant from the function and its inverse.

Click on the blue point an drag it to change the figure
Note that the blue point on the line of symmetry is always equidistant from both functions.
 Manipulative 2  Line of Symmetry Between Inverse Functions Created with GeoGebra. 
