parabola

Let  the point  on the ground directly  below the  center of the top of the arch  = (0,0)

Then  the points  ( 0, 25)  ( 20, 0)  and (-20, 0)  are  on the graph of the parabola

We  have  this

25  = a ( 0 - 20)  ( 0 + 20)

25  = a (-400)

a = 25 / -400  =  -1/16

So  we  have  the  form

y = (-1/16) ( x- 20) ( x + 12)

8  feet from the center  is the  point  (8,0)

So...the  height at that point can be found as

(-1/16) ( 8 + 20) (8 - 20)  =

(-1/16) (28) (-12)  =

(12/16) (28) = 

(3/4) (28)  =

3 (28/4)  = 

3 * 7  =  

21 ft