SOLUTION: This is another question about parabola. A tunnel is to built to allow 2 lanes of traffic to pass from one side of a mountain to the other side. The largest vehicles are trucks,

Question 752606: This is another question about parabola.
A tunnel is to built to allow 2 lanes of traffic to pass from one side of a mountain to the other side. The largest vehicles are trucks, which can be considered as rectangles 5m wide and 7m high.
Investigate the cross-section of a parabolic tunnel and find a possible equation to represent it. Allow some space so trucks do not bump into each other or the sides of the tunnel. it have to be use algebra and geometry to solve this problem
many thanks
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Question you want to find is, how far should one truck be from the oppositely moving truck, and how far should a truck be from the tunnel surface. This feels like it's open-ended.

Let's imagine just to be simple, you want 1 meter between trucks of opposing travel direction and half meter from truck top horizontally to the tunnel and one meter from truck bottom to the tunnel bottom. We are not sure yet where the vertex is.

Try drawing that description.

The x-axis has an origin as the middle line of the road and to the right on the bottom is a point (5+1/2+1,0) and to the left on the bottom is (-(5+1/2+1),0). These are the points, (6.5,0) and (-6.5,0).
At the top of truck level, there are points on the parabola, on the right, (5+1/2+1/2,7) and on the left is (-(5+1/2+1/2),7). These points are (6,7) and (-6,7).
This parabola may be imagined opening down, and as described, centered at x=0. We then have a form, , we know a<0, and we have two (or four?) points to work with. Maybe this will be enough.

Just those two points (the negative x values do not help) are not enough. We need one more point. One suggestion is just pick an arbitrary vertex top-most point and work with that. It along with one of the other points would/should help get a value for 'a'. ...and also for k.
Just a guess, try picking a vertex of about (0,11) and see if this helps to get an 'a' and a 'k'.

...
Yes, this should give you something.
and applying chosen description point (6,7) will allow finding a value for a. Top of tunnel can be located 11 meters above the middle of the road.
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