Put the origin of the coordinate system at the highest point of the arch, the axis "y" directed vertically up.

so the the origin of the coordinate system will be THE VERTEX of the parabola.


You have y = ax^2 as the equation of the parabola with the negative unknown coefficient "a".


The equation for "a" is

y(12) - y(16) =  -  = 6,     (1)

saying that  at the distance of 12 = 16-4 meters from the side the height of the tunnel is 6 meters.


Then  a =  =  =  = .


Hence and finally, the equation of the parabola is

y =  

in this coordinate system.   // And, although the problem does not ask about it, the height of the tunnel is   = 13.71 meters.