Question

a parabolic bridge over a road is 4 meter tall 4 meter wide and 5 meter long determain the maximum height of a 2 meter truck can drive under the bridge

Answer 1

I am assuming that your somewhat vague language means that the parabola can be described by

y = 4-ax^2

and that the parabola intersects the road below at x=2.5

So, y = 4-(16/25)x^2

Now, assuming you mean a truck which is 2m wide and is driving right down the center line, that means x=1, so

y(1) = 4 - 16/25 = 84/25 = 3.36m

If the truck is driving just to one side of the center line, that means x=2, and

y(2) = 4 - (16/25)(4) = 36/25 = 1.44m

I still can't factor in what "4m wide" means for the bridge. The width of the pavement? That makes no difference on level ground. The problem is very poorly worded.