Domain and range of locus formed from parametric equations

Question

\begin{cases} x = t^2 + 2t\\ y = 4(t+1)^2 \end{cases}

Determine the cartesian equation of the locus? What is the domain of the locus?

Note: I have found the cartesian equation: $y=4x+4$ I am just not sure if their is a restriction on the domain.

Answer 1

$$x = t^2 + 2t = (t+1)^2 - 1 \ge -1 \,\forall t \in \Bbb R$$ Hence the required domain is $[-1,\infty)$.