# Math Help - Parabolic Arch

1. ## Parabolic Arch

If you can't read it, "A horizontal brige is in the shape of a parabolic arch. Given the information in the picture below, what is the height of the arch 2 feet from the shore?

Thank you

2. ## Re: Parabolic Arch

Originally Posted by BrendaB
If you can't read it, "A horizontal brige is in the shape of a parabolic arch. Given the information in the picture below, what is the height of the arch 2 feet from the shore?

Thank you
Hi BrendaB!

You would use x-h=8, which is the distance from the origin labeled as B.

3. ## Re: Parabolic Arch

If you put the left hand corner at the origin, then you have three points, namely the two x intercepts (0, 0) and (20, 0), and the turning point (10, 10).

The turning point form of the equation will be the easiest to use, $\displaystyle y = a\left( x - h \right)^2 + k$. You have (h, k) = (10, 10) and after substituting these and another point as (x, y) you can get the value of a.

Once you have the equation of your curve, set y = 2 and solve for x.