A parabolic arch - Math Central

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Question from Muhammad, a student:

An arch over a road has a parabolic shape it is 6 meter wide at the base and is just
tall enough to allow a truck 5 meter high and 4 meter wide to pass
a):
assuming that the arch has an equation of the form y=a(x)^2+b use the given
information to find a & b. explain why this assumption is reasonable.
b):
sketch the graph of arch equation

Hi,

This is my diagram of the rear of the truck as it passes under the arch.

arch

The X-axis is along the surface of the ground and the Y-axis passes through the apex of the arch. What are the coordinates of the points $P$ and $Q?$ Substitute the coordinates of $P$ and $Q$ into $y = ax^2 + b$ and solve for $a$ and $b.$

Penny

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