There is no need to explain that the parabola is opened down in this problem.


So, let assume that the origin of the coordinate system is established at one edge of the tunnel.
Then the other edge is at x= 20 meters.


So, our parabola has two intersections with x-axis: at x= 0 and x= 20.


Thus the parabola has two zeroes, 0 and 20. Therefore, we can write it in the form

    y = a*(x-0)*(x-20) = a*x*(x-20),


where "a" is some real coefficient, now unknown.


To find "a", use the fact that  y(4) = 16 meters, which is given.  So

    a*4*(4-20) = 16,   or

    4a*(-16) = 16, 

    -4a      =  1,

      a      = -1/4 = -0.25.


Thus, the parabola is

      y = -0.25x*(x-20).


Its vertex is half-way between 0 and 20, i.e. at x= 10.


Therefore, the highest point of the parabola is  y(10) = -0.25*10*(10-20) = -0.25*10*(-10) = 25.


ANSWER.  The height of the tunnel is 25 meters over the ground level.