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.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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.      Log On


   

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) About Me  (Show Source):
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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= Y%5Btop%5D = 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:  Y%5Bbottom%5D = -(3.5)^2 + 3 = -12.25 + 3 = -9.25 m.



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


    H = Y%5Btop%5D - Y%5Bbottom%5D = 3 - (-9.25) = 12.25 m.     ANSWER