SOLUTION: Owachomo Natural Bridge is found in National Bridges Natural Monument in Utah. If the origin is located at one end of the natural arch, the curve can be modeled by the equation h=-

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Question 366328: Owachomo Natural Bridge is found in National Bridges Natural Monument in Utah. If the origin is located at one end of the natural arch, the curve can be modeled by the equation h=-0.043d^2+2.365d where h meters is the height of the arch, and d meters is the horizontal distance from the origin.
a) what is the maximum height of the arch, to the nearest hundredth of a meter?
b) What is the width of the arch at the base?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
anytime you have a quadratic equation such as the one you pose
there are several ways to answer your question.
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1) complete the square
h=
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So the maximum height is 32.51 meters when d=55/2=27.5 meters
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Another way to figure this out is to remember that a quadratic equation ofthe form y=ax%5E2%2Bbx%2Bc has its vertex at x=-b/(2a) and that the vertex (minimum if a>0 or maximum if a<0) is found by substituting x=-b/(2a) back into y=ax%5E2%2Bbx%2Bc
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so in your equation a=-0.043 and b=2.363
since a<0 the vertex is a maximum and its found at x=-2.363/(2*(-0.043))=27.5
so substitute x=27.5 in y=-0.043x%5E2%2B2.363x yielding
y=-0.043%2A27.5%5E2%2B2.363%2A27.5=32.46
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some rounding error between this method and the previous method, otherwise the same answer.