# Trig

A bridge is built in the shape of a parabolic arch. The bridge has a span of s= 160 feet and a maximum height of h= 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.

10=
30=
50=

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1. If it has a span of 160', then the equation of the parabola is
f(x)=ax(160-x)
where a is a constant, and x=0 and x=160 are the zeroes which correspond to points where the arch reaches ground/water.
The constant "a" can be found by the fact that f(80)=25.

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2. 10 feet= 24.61 ft
30 feet= 21.48 ft
50 feet= 15.23 ft

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3. Yes, the answers are all correct.
You have also correctly taken the origin at the centre of the span, which is logical since the question requires the height at distances from the centre.

Check that at negative distances the heights are the same.

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