SOLUTION: The curve of the tunnel is represented by the equation y= - x^2+3.The width of the road is 7m. Calculate the maximum height, in m,of the tunnel.

Question 1136732: The curve of the tunnel is represented by the equation y= - x^2+3.The width of the road is 7m. Calculate the maximum height, in m,of the tunnel.
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
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The shape of the tunnel is represented by the downward parabola equation


    y = -x^2 +3.


The parabola has a vertex at elevation y=  = 3.



First, we need to determine the bottom elevation of the tunnel  y, where x = 7/2 = 3.5 m.


It is easy to do:   = -(3.5)^2 + 3 = -12.25 + 3 = -9.25 m.



Now, the height of the tunnel is the difference of two elevations 


    H =  -  = 3 - (-9.25) = 12.25 m.     ANSWER

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