This is actually a little worse than shop math. I have solved this; will confirm
the first correct answer.

Find an equation of a conic (2nd order function) which goes through the points
(0,0) (2,0.75) and (2.5,5) and is tangent to the X axis at (0,0) and is nearly
vertical at the point (2.5,5). Put it in the form y = F(x); in other words with
y alone on the left hand side of the equation.

GWE

Find an equation of a conic (2nd order function) which goes through the points

GWE