Question

Construct a polynomial function with the given zeros (0, touches, 1, touches, 2 touches)

Answer 1

f(x) = x^2 (x-1)^2 (x-2)^2

Answer 2

A polynomial function will CROSS when the multiplicity of the FACTOR is ODD (1,3,5....) and will TOUCH when the multiplicity of the FACTOR is EVEN (2,4,6...). So take the zeroes, change the sign of the number and turn it into a facotr (i.e., zero of 1 becomes (x-1) then raise the factor to an appropriate ODD or EVEN power...