Question

The curvature of the Tacoma Narrows Bridge in

Washington is in the shape of a parabola. In
the given function, x represents the horizontal
distance (in meters) from the arch's left end
and y represents the vertical distance (in
meters) from the base of the arch. What is the
width of the arch?
f(x) = -0,016 (x - 52.5)2 + 45
m
(Round to the nearest integer as needed.)

Answer 1

Width of the arch = 105 m

Explanation:

Function representing the width of the arch,

f(x) = -0.016(x - 52.5)² + 45

where x = width of the base of the arch or horizontal distance from arch's left end

f(x) = vertical distance of the arch

From the given quadratic function, vertex of the parabola is (52.5, 45).

Coordinates of the vertex represents,

Height of the arch = 45 m

Half of the horizontal distance from the left end = 52.5 m

Therefore, width of the bridge = 2(Half the width of the bridge from left end) = 2×52.5

= 105 m

Therefore, given bridge is 105 m wide.