"At the start of this section of the "Colossus", its height off the ground is 150m " so y(0)= a= 150.
"60m Horizontally along, the "Colossus" has dipped to a height of just 30m" so .
From the way this is worded, I think we can assume this is a minimum height so the derivative must be 0:
"It peaks again at a horizontal distance of 180m". We aren't given the height but again the derivative must be 0: .
"and features another dip at a horizontal distance of 300m. " Again we aren't told the height but the derivative must be 0: .
Five eqations to solve for a, b, c, d, and e.