Graph the plane curve formed by the parametric equations and indicate its orientation.
$x\left(t\right)=2t-1$; $y\left(t\right)=2\sqrt{t}$
$t\ge 0$

• A.
• B.
• C.
• D.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the parametric equations given: x(t) = 2t - 1 and y(t) = 2√t, with the condition t ≥ 0. These equations describe the x and y coordinates of a curve as functions of the parameter t.
2. Step 2: Determine the range of t. Since t ≥ 0, the parameter starts at 0 and increases. This will help establish the orientation of the curve.
3. Step 3: Calculate specific points on the curve by substituting values of t into the parametric equations. For example, for t = 0, x(0) = -1 and y(0) = 0; for t = 1, x(1) = 1 and y(1) = 2; for t = 4, x(4) = 7 and y(4) = 4.
4. Step 4: Plot the calculated points on a graph and connect them smoothly to form the curve. Ensure the orientation is indicated by arrows showing the direction of increasing t.
5. Step 5: Analyze the graph to confirm the shape and orientation. The curve starts at (-1, 0) and moves to the right and upward as t increases, following the calculated points and the parametric equations.