Posted by **EVJ** on Monday, July 18, 2011 at 9:16am.

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=

- Trig -
**MathMate**, Monday, July 18, 2011 at 9:42am
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.

Post your answer for a check if you wish.

- Trig -
**EVJ**, Monday, July 18, 2011 at 9:50am
10 feet= 24.61 ft

30 feet= 21.48 ft

50 feet= 15.23 ft

- Trig -
**MathMate**, Monday, July 18, 2011 at 10:17am
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.

## Answer this Question

## Related Questions

Math/Algebra - A bridge is built in the shape of a semi elliptical arch. It has ...

Math - The underside of a bridge has a shape of a parabolic arch. It has a ...

Algebra (word problems) - Studying help! Flights of leaping animals typically ...

11th grade - The arch of a bridge is a semi ellipse, the span is thirty feet and...

AP Calc - The picture to the right shows the Ben Franklin Bridge which stretches...

college algebra - I have been stuck on this problem for over a week and I don't ...

algebra - You live near a bridge that goes over a river. The underside of the ...

algebra - You live near a bridge that goes over a river. The underside of the ...

Writing - How can I end this? ____ The bridge I made a model of is the Sydney ...

math - How do I draw this out I am confused? The bridge forms parabolic arch. ...