my professor gave practice problems for an upcoming midterm, and one is to find a differentiable parametrized curve with trace $y = |x|$ with $-1 \leq x \leq 1$.
My thinking is that I should find a parametrization with $\alpha'(0) = (0,0)$ and of course $x = -y, x = y$ for negative and positive $x$ respectively, however I cannot think of such a curve. Could someone help me out?