An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?
The origin of the coordinate plane is taken at the vertex of the arch in such a way that its vertical axis is along the negative y –axis.
This can be diagrammatically represented as
The equation of the parabola is of the form x2 = -4ay (as it is opening downwards).
It can be clearly seen that the parabola passes through point 
Therefore, the arch is in the form of a parabola whose equation is
When, y = -2, 
Hence, when the arch is 2m from the vertex of the parabola, its width is approximately 2.23m.
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