Unfortunately, we cannot see your drawing. Answer would be only speculation.
"A horizontal bridge is in the shape of a parabolic arch" -- What does that mean? Is it horizontal or is it parabolic? A drawing would clear up this confusion.
A horizontal bridge is in the shape of a parabolic arch. Given the information below, what is the height h of the arch 2 feet from shore?
*width across bridge (from one side of the parabola to the other side of the parabola) is 20 feet
*The height of the arch (the vertex of the parabola under the bridge to the water below) is 10 feet
*the height h we want is located under the bridge itself 2 feet from the shore
Center your parabola at the origin.
You can use the formula to find the parabola equation with the given info.
h=0, k=10, y=0, x=10
Plug them in and solve for a. Then you have your equation.
Then just plug in x=8 to find the height at 2 feet from the end.
This second person to whom you are referring took a wild stab at what you meant. If this guess was close enough to be of benefit to you, that is great, but this does NOT mean that you provided sufficient information. If you simply would have answerd my objections, there would have been no guessing involved. Please make an effort to provide COMPLETE problem statements and any necessary drawings.
I meant nothing bad by my reply. I think you are a great mathematician.
The people who post questions here (LIKE ME) do not have a solid relationship with math.
I have read your replies and consider you to be one of the best mathematicians online.
I thank you and sorry for hurting your feelings.