differential geometry : paramterization of an absolute value function

j.ayoub

I need help with the following question:

for the absolute value function y = |x-1| in R2

a) A parametrization of the curve
b) a four times differentiable parametrization of this curve
c) is there a regular parametrization

Can I parametrize this curve by setting x = t^2 --> y = |t^2 -1|?