Hi
An arch is in the shape of a parabola. 
It has a span of 208 meters and a maximum height of 26 meters.
 y = ax^2 + 26   (Sry, no clue where the 42 came from)
  a = -26/(104)^2 = -25/10816 = -1/416
 y = 
 y(55) =  18.73m rounded to nearest hundredth

Wish You the Best in your Studies.
    

You have this instruction to place the origin at halfway between the arch's feet).


It means that the parabola is open downward and its vertex is at the point  (0,26),

while the x-intercepts are 104 =  meters away from the origin.



THEREFORE, you write the equation of the parabola in the form

    y(x) = -ax^2 + 26


and you find then the value of the coefficient "a" from the condition  y(104) = 0, which is


    -a*104^2 + 26 = 0,   or


     a =  =  = .


So, the parabola equation is  

    y(x) = -  + 26      ANSWER


CHECK.   y(0) = 26;    y(104) = -  + 26 = -  + 26 = -26 + 26 = 0.    ! Correct !



    


                                   y(x) = -  + 26


55 meters from the center, the height of the arch is

          y(55) = -  + 26 = 18.73 meters (rounded).