If a trailer is 9m wide and stands 3.2m tall, measured from the ground to the top of the trailer, will it fit under the bridgeA hauling company needs to determine whether a large house trailer can...

If a trailer is 9m wide and stands 3.2m tall, measured from the ground to the top of the trailer, will it fit under the bridgeA hauling company needs to determine whether a large house trailer can be moved along a highway that passes under  a bridge with an opening in the shape of a parabolic arc, 12m wide at the base and 6m high in the center. This is a quadratic application. Please include all steps. I am aware of the fact that this question has already been posted, but the way I have set up the question is different. For my graph I have the x-intercepts to be (0,0) and (12,0) instead of having (-6,0) and (6,0). I know the vertex is (6,6) as well.
Expert Answers
hala718 eNotes educator| Certified Educator

f(x)= ax^2+bx + c

f(0) = 0 ==> c = 0

f(12)= 0 ==> 144a+12b= 0==> 12a+b= 0==> b= -12a

f(6)= 6 ==> 36a+6b = 6 ==> 6a+b= 1==6a -12a=1==> -6a=1

==> a = -1/6

==> b= -12*-1/6 = 2

==> Then the equation is:

f(x)= (-1/6)x^2 +2x

 

Now we will assume that the trailer passes through the bridge fro the middle.

The width of the trailer is 9 .

==> Then the points where the trailer passes is between 6-4.5 and 6+4.5 ==> Then the trailer passes between x= 1.5 and x= 10.5

Now to make sure that the trailer passes under the bridge we will find the height of the parabola at the points 1.5 or 10.5

==> f(1.5)= 2.625

Then the height at the between the points 1.5 and 10.5 is 2.625

But the trailer height is given 3.2.

Then the trailer can not fit under the bridge.