Is there a first- or second-degree polynomial that takes the values $100,90,70,40,0$ for the variable values $0,1,2,3,4$ respectively?
It is easy to calculate that a quadratic polynomial satisfying the conditions exists and can be written as follows: $y=$ $-5 x^{2}-5 x+100$. It must be proven that a linear polynomial does not exist. It is not sufficient to say that if the points are plotted on the coordinate system: it is visible. (Appearance can often be deceiving.)