a polynomial function that might have the given graph more t

a polynomial function that might have the given graph. (more than one answer may be possible)

Solution

we see that graph intersects x-axis at x=0, 1, 2
so possible factors are (x-0)(x-1)(x-2)
since grpah touches x=1 and turns back in same direction so multiplicity of root x=1 must be even that is x=1 may repeat 2 times or 4 times or 6 times etc.
I will consider x=1 repeates twice
so required polynomial will be
f(x)=(x-0)(x-1)(x-1)(x-2)
you can multiply those factors if you need answer without parenthesis