Equation of a Bridge

May 2010
1
0
Hi, how would I find the equation of a bridge (parabola) if the river is 18m wide, and the arch of the parabola must be anchored on the ground 3m back from the riverbanks. The bridge's arch must reach a maximum height of 22m above the river. Thanks.
 

earboth

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Hi, how would I find the equation of a bridge (parabola) if the river is 18m wide, and the arch of the parabola must be anchored on the ground 3m back from the riverbanks. The bridge's arch must reach a maximum height of 22m above the river. Thanks.
1. Place a coordinate system with it's origin in the middle of the river.

2. Then the bridge arc is a symmetric parabola with it's vertex at V(0, 22) and the zeros at ((9+3),0) or (-(9+3),0).

3. The general equation of such a parabola is:

\(\displaystyle p(x)=a x^2+c\)

Determine a and c (<-- :D )