I have chosen to include a list of instructions on how to use GSP to construct such a parabola.

segment constructed in step 5 will intersect (F).

The final construction should resemble the following picture.

Once these preliminary constructions are completed, it is then necessary
to animate point C along line j. One way to show the construction of the
parabola is to trace point F. By doing so, the set of all points eqidistant
from the dirrctrix and the focus is being constructed.

An alternative approach would be to perform the same animation, but trace line k such that the envelope of lines formed by this animation will construct the parabola. Indeed, these lines are tangent lines to the parabola at any given point.