What is an equation of a parabola with a vertex at the origin and directrix x=4.75?

An equation for the parabola would be y²=-19x.

Since we have x=4.75 for the directrix, this tells us that the parabola's axis of symmetry runs parallel to the x-axis. This means we will use the standard form

(y-k) ²=4p (x-h), where (h, k) is the vertex, (h+p, k) is the focus and x=h-p is the directrix.

Beginning with the directrix:

x=h-p=4.75

h-p=4.75

Since the vertex is at (0, 0), this means h=0 and k=0:

0-p=4.75

-p=4.75

p=-4.75

Substituting this into the standard form as well as our values for h and k we have:

(y-0) ²=4 (-4.75) (x-0)

y²=-19x