Answer:
To find the quadratic equation:
Assume any point (x, y) on parabola.
Use the distance formula i.e, 
Distance between (x , y) and focus
is:

Now, the distance between (x, y) and directrix of y =
is:

On the parabola these distance are same;
= 


or

Simplify:


Simplify:
or

Divide both sides by 16 we get;


or

Simplify:

therefore, the equation of the quadratic is; f(x) =negative one sixteenthsx^2 − one half x + seven-fourths.