# Math Help - Calc Cartesian Equation

1. ## Calc Cartesian Equation

A curve is parametrized by x=t, y=the square root of (t+2), t is greater than or equal to -2.
Write a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve?

2. Hello, SoYah!

A curve is parametrized by: . $\begin{array}{cccc}x\:=\:t & {\color{blue}[1]}\\ y\:=\: \sqrt{t+2} & {\color{blue}[2]}\end{array}\;\:\text{ for }x \geq -2$

(a) Write a Cartesian equation for a curve that contains the parametrized curve.

Substitute [1] into [2]: . $y \:=\:\sqrt{x+2} \quad\Rightarrow\quad x \:=\:y^2-2$

This is a parabola that opens to the right, vertex at (-2,0).

(b) What portion of the graph of the Cartesian equation is traced by the parametrized curve?

The parametric equations determine the upper half of the parabola.