First, lets draw a graph of some function that has this properties:
in our case, we know that if our function is a polynomial and has a bounce in some point, that means that the point that its bounces is a even degree root, wich means that is a double root, or a fouth root...
So, if we construct a polinomial with the form:
[tex]f(x)=(x-(-2))\times(x-3)\times(x-5)^2[/tex]
Is a polynomial that has roots in x=3, x=-2 and double root in x=5, meaning that bounces in x=5.
