There is no escape...believe it or not. Mathematics is everywhere.
Vertical Curve Problem
Given: Two tangents to a roadway profile intersect at an elevation of 100. The first tangent is at a 2% uphill
grade and the second tangent is a -5% downhill grade. Calculate the equation of
a 200 ft parabolic curve connecting the two tangents and the elevation at the
mid point of the curve. Let the “x” origin be at the beginning of the curve.
The equation of the tangent lines are y = -0.05x + 105 and y = 0.02x + 98 but I'm not sure where to go from there.