Bro here is the how i did it. But just a word of advice. this is way way beyond the scope of GMAT. Gmat will never ask you how to write a equation of a parabola for sure...

equation of parabola

ax^2+bx+c=y

from 1st coordinate you get (-1/2,5/8)

5=2a-4b+8c -------(I)

from 2nd coordinates (1/2,1/8) you get

1=2a+4b+8c --------(II)

subtracting these two equations you will get value of b = -1/2

now you need to know another concept which is called axis of symmetry for a parabola.

axis of symmetry is given as x=-b/2a

its given in the question as 1

hence you will get b=-2a ------(III)

solving 3 equations you will get values of a= 1/4, b=-1/2 and c=5/16

you can form the equation of parabola.

questions asks value for y for x= 5/2

substituting values given above you get

y =1/4(25/4)-1/2*5/2+5/16
y= 5/8

this can also be done graphically.

I actually have seen GMAT parabola questions, so it's good to know this formula! Remember when we have three equations with the same three unknowns, we can always solve.

When they give us the symmetry is y = 1, we know then that -b = 2a, and b = -2a, so we will be able to substitute and solve. Nice job, Force5!