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If a trailer is 9m wide and stands 3.2m tall, measured from the ground to the top of...
Topic: MathIf 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.
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High School Teacher
Best answer as selected by question asker.
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.
Posted by hala718 on May 15, 2012 at 11:55 PM (Answer #1)
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