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 bridge (more info below)? A 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 don't understand how to do this problem.

Expert Answers

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We will assume that the arc is a parabola facing down.

Then the equation of the parabola would be:

f(x) = -ax^2 + bc + c

Now we will assume that the highest point is on the y-axis. Then the point ( 0,6) is the maximum point.

Now we will assume that the endpoints of the parabola is on the x-axis where the distance is 12 m.

Then the endpoints are ( 6, 0) and (-6, 0)

We will substitute and determine a, b , and c.

First we will substitute ( 0, 6)

==> f(0) = c = 6

==> c = 6

Now we will substitute 6 and -6/

==> f(6) = -36a + 6b + 6 = 0

==> -6a + b + 1 = 0 .............(1)

f(-6) = -36a - 6b + 6 = 0

==> -6a -b + 1 = 0............(2)

Now we will add (1) and (2).

==> -12a + 2 = 0

==> a = 1/6

==> b= -6a+ 1 = 0

==> b= 0

==> f(x) = -(1/6)x + 6

Now we need to determine if the trailer of 9 ft wide can fit under the bridge.

If the trailer drive exactly in the middle of the bridge then it will be between the points ( 4.5, 0) and ( -4.5, 0).

Now we need to find out the height of the bridge at these points.

We will substitute with f(4.5).

==>f(4.5) = -(1/6) (4.5)^2 + 6 =  2.635.

Then, the height of the bridge at the points (4.5, 0) is 2.635 m.

But the trailer height is 3.2

Then, the trailer can not fit under the bridge.

Approved by eNotes Editorial Team

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