## Precalculus (6th Edition) Blitzer

The different sets of parametric equation are: $x=t\text{,}\,\,y={{t}^{2}}+4\,\,\text{ and }\,\,x=t+1\text{,}\,\,y={{t}^{2}}+2t+5$ (other answers are possible.)
Let us assume $x=t$, Then, $y={{t}^{2}}+4$ The solution set for y remains the same for both negative and positive values. Let $x=t+1$ Now, \begin{align} & y={{(t+1)}^{2}}+4 \\ & y={{t}^{2}}+2t+1+4 \\ & y={{t}^{2}}+2t+5 \\ \end{align} The solution set for y remains the same for both negative and positive values. Note that many different sets of parametric equations are possible. Choose any two from them. Thus, $x=t\text{,}\,\,y={{t}^{2}}+4\,\,\text{ and }\,\,x=t+1\text{,}\,\,y={{t}^{2}}+2t+5$ are two different sets of parametric equations.