You are designing a simple roller coaster for an amusement park. The model is given in the figure. It is composed of two lines and two parabolas (blue and green part). You should design parabolic parts and total length of the rails for these parts should be approximately 150 m(± 5). Some distances are given in the figure and you should satisfy these conditions.

The approximate length of a parabolic curve in 1st quadrant (a x²+b x+c) on interval [x₁, x₂] can be calculated by a formula


a(x₁²+x₂²)+b(x₁+x₂)+{b²/2 a} | where -b\2a ∈ x₁, x₂


Now your task is to design this roller coaster with functions (as a piecewise function) in 1st quadrant in any math program like desmos, geogebra etc with given conditions.


After you completed your model calculate the maximum height that this roller coaster will reach. Remember that the higher it goes the more fun it will be