Problema Solution
A bridge over a river is supported by a parabolic arch. The arch is 200m wide at water level and the maximum height of the arch is 80m.
a)draw a picture of the arch on a coordinate plane, placing the orgin at the vertex of the parabola. find the equation of this arch
Answer provided by our tutors
the description is of a parabolic arch with the following three points, shown as (x,y) pairs:
(-100, 0), (0, 80) and (100,0)
we solve and find this equation:
y=-(1/125)x^2 + 80
to place the origin at the vertex of the parabola, the points become:
(-100, -80), (0, 0) and (100, -80)
the equation then becomes:
y = -(1/125)x^2
the equation of the arch, with origin at the vertex of the parabola, is y=-(1/125)x^2