SOLUTION: The shape of a supporting arch can be modeled by h(x) = -0.03x^2 + 3x,where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base

Question 289507: The shape of a supporting arch can be modeled by h(x) = -0.03x^2 + 3x,where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base of the arch in meters. Find the maximum height of the arch.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The shape of the arch is that of a parabola (opening downward, of course)
The x-coordinate of maximum height of a parabola (the vertex) is given by:
where the a and b come from the standard form for a parabola: Here, the given equation is: , so a = -0.03 and b = 3
Making the appropriate substitutions, we get:

Now substitute this into the given equation to find the maximum height at x = 50m.:

meters. This is the maximum height of the arch.
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