Draw a coordinate system on the plane with the x-axis at ground level and the y-axis the axis of symmetry of the parabola. The width of the bridge is 192 feet so the parabola crosses the x-axis with x-coordinates ± 192/2 = ± 96. The maximum height occurs at x = 0 so the vertex of the parabola is (0, 30).

Since the curve is a parabola which opens downward its equation can be written f(x) = ax^2 + bx + c.

Since (0, 30) is on the curve f(0) = 30 this means c = 30

f(96) = f(-96) that is 96b = -96b => b = 0

f(96) = 0

a*96^2 + 30 = 0

a = - 30/(96^2) = - 5/1536

for x = 15 we have

f(15) = - (5/1536)*(15^2) + 30

f(15) = 29.2676 feet

the height of the ark at 15 ft from its center is 29.27 ft.