Question 1062337: A parabolic bridge is built across the water. It is 50m long, and its highest point is 4.5m high.
a)What is the equation of the graph, where y= The height above the water, and x=the horizontal distance from the origin.
b)A floating platform 20m wide is towed under the bridge. What is the greatest height of the deck above water level if the platform is to be towed under the bridge with at least 30cm horizontal clearance on either side.
Any help would be appreciated :)
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Where is your origin? How high is the base of the bridge above the water?
With just the given, you might put the bridge base at the water level and assign the origin at the middle between the two sides of the water (stream or creek or river). This way, your zeros are at (-25,0) and (25,0), and vertex as maximum height is (0, 4.5). Your unknown constant factor in  can be determined.
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! The solutions, or roots are  and 
and half-way between these points at  ,
I have the point ( 25, 4.5 )
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(a)
The general equation would look like:
( I need the squared term to be negative, since
that gives me a peak and not a dip )
The solutions are:
( 0,0 )
and
( 50,0 )
(1) 
--------------------------
The peak, or vertex, is at ( 25, 4.5 ), so
(2) 
Plug (1) into (2)
(2) 
(2) 
(2) 
(2) 
and
(1)
(1) 
(1) 
------------------------------------
So, the equation is:
( Note there is no constant term because the
parabola goes through ( 0,0 ) )
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(b)
 m
There is  m clearance on both sides
So, I have the points
( 15, y[1] ) and
( 35, y[2] ) as points on the bridge that are
directly above the ends of the floating platform
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( 15, y[1] )
 m
---------------------------------
( 35, y[2] )
 m
( this makes sense because the platform is
exactly in the middle )
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If you want  m on each side,
then what value of  goes with 
or 
------------------------
 m
This is the height of the platform that gives me  cm
clearance on the sides.
The points on the platform are below the bridge, and they are at
( 15, 3.751 ) and
( 35, 3.751 )
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I would definitely get a 2nd opinion
I coiuld easily miscalculate
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Here's a plot of my equation:
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