A parabolic arch bridge has a 60ft base and a height of 24ft. Find the height of the arch at a distance of 5, 10, and 20 ft from the center

Answer 1

let the vertex of the parabola be (0,60)
its equation would be
y = ax^2 + 60 , but (30,0) and (-30,0) would also lie on it

0 = a(900) + 60
a = -60/900 = -1/15

equation of bridge is
y = (-1/15)x^2 + 60

so when x = 5
y = (-1/15)(25) + 60 = 175/3 ft
or 58 1/3 ft
or appr 58.33 ft

repeat for x = 10 and x = 20