The most puzzling Math. word problem so far

The problem (printed):

The arch of a stone bridge has the shape of part of a parabola 20 ft high at its highest point above the water and 80 ft wide at water level.
How high is the arch above the water at a point 10 ft in from one of its ends ?

Please not only explain your answer in details but also try to make me, as a student, imagine it , make me understand it.

The bridge is a down-opening parabola. Let the vertex be (0, 20), then its equation is
y = ax² + 30
and the endpoints of the bridge are (-40, 0) and (40, 0).

To solve for a, plug the coordinates of an endpoint into the equation.
0 = 1600a + 20
-20 = 1600a
a = -1/80

The equation of the parabola becomes
y = (-1/80)x² + 20

When x = ±30, y = (-1/80)x² + 20 = 8.75.
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Vertex (h, 20)

k = 20

x1 = 0
x2 = 80

h = 1/2 (x1 + x2)
h = 1/2 (0 + 80)
h = 1/2 (80)
h = 40

x = 80
y = 0

y = a (x - h)² + k:

0 = a (80 - 40)² + 20
0= a (40)² + 20
0 = a(1600) + 20
0 = 1600a + 20
1600a = - 20
a = - 20 / 1600
a = - 1/80
a = - 0.0125

Equation:

y = - 0.0125 (x - 40)² + 20

When x = 10 ft.,

y = - 0.0125 (10 - 40)² + 20
y = - 0.0125 (- 30)² + 20
y = - 0.0125 (900) + 20
y = - 11.25 + 20
y = 8.75

At a height of 10 ft., the arch is 8.75 ft. above the water.