The parabolic arch of a bridge over a one-way road can be described by the equation y = -x^2 + 6, where x and y ar emeasured in metres. A transpor truck is 3m wide and 3.5m high. What is the maximum clearance of the truck's top corners if it passes under the bridge?

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The parabolic arch of a bridge over a one-way road can be described by the equation y = -x^2 + 6, where x and y ar emeasured in metres. A transpor truck is 3m wide and 3.5m high. What is the maximum clearance of the truck's top corners if it passes under the bridge?

Mathematics
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This is an Optimization problem.
so you want the max distance from the top corner of truck to arch ??
distance from top center of arch to top corner of truck is 2.915 m

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Other answers:

Yes How were you able to work that out?
d^2 = 2.5^2 + 1.5^2
How did you come to this equation?
truck is 3.5m so vertical distance from top is (6-3.5) = 2.5 truck is 3m wide, 1.5m on either side of center line imagine a triangle formed from right side of top of truck to top center of arch d is hypotenuse and is the longest distance from arch to truck top corner

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