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**HallsofIvy** The problems says "may be represented by a 4th degree equation. That is $\displaystyle y= a+ bx+ cx^2+ dx^3+ ex^4$ where x is the horizontal distance and y the height. You need to find the 5 coefficients so you need 5 equations.

"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 $\displaystyle y(60)= 150+ 60b+ 60^2c+ 60^3d+ 60^4e= 30$.

From the way this is worded, I think we can assume this is a minimum height so the derivative must be 0: $\displaystyle b+ 2(60)c+ 3(60^2)d+ 4(60^3)e= 0$

"It peaks again at a horizontal distance of 180m". We aren't given the height but again the derivative must be 0: [tex]b+ 2(180)c+ 3(180^2)d+ 4(180^3)e= 0.

"and features another dip at a horizontal distance of 300m. " Again we aren't told the height but the derivative must be 0: [tex]b+ 2(300)c+ 3(300^2)d+ 4(300^3)e= 0.

Five eqations to solve for a, b, c, d, and e.