1. With reference to the example, determine the expression of the function $y = f(x)$ and the equation of the curve $\Lambda$, so as to be able to perform a test and verify the operation of the machine.
You are asked to construct a tile with a more elaborate design that, in addition to respecting conditions a), b) and c) described above, has $f'(0) = 0$ and the area of the coloured part equal to 55\% of the area of the entire tile. For this purpose, consider polynomial functions of second and third degree.