At right is the tunnel entrance that runs through Castle Hill in Budapest, Hungary.

-a If the maximum height of the tunnel is the
same as its maximum width, 9.8 meters,
determine a quadratic model to represent
the tunnel
-b State a geometric model that could be used to
represent a truck passing through the tunnel.
-c If a typical truck has a width of 2.62 m,
determine the height limitation that should
be put on these trucks if they are going to
travel through the tunnel safely. State any
assumptions that you made and be sure to
show all of the steps in your solution.
-d Because its length is almost 350 meters,
a truck stopped in the tunnel would need
enough room for the passenger door to open
fully. Suppose a truck with a width of 2.6 m
and height of 3.4 m is stuck in the right lane
of the tunnel by the center line. The top of
the driver's door is 0.2 m below the top of the
truck, and the door opens 0.8 m to the side.
Show that the door can open fully, showing
all of your steps.
-e Determine how close to the side of the tunnel
the truck could be in d be and still be able to
open the passenger door.
-f Describe some issues/concerns that you
think architects take into account when
modelling a tunnel before its construction