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. Identify the parametric equations given: x(t) = 2t - 1 and y(t) = 2\sqrt{t}, with the condition t \geq 0.
2. Determine the range of t to plot the curve. Since t \geq 0, start with t = 0 and choose a few positive values for t to calculate corresponding x and y values.
3. Calculate the x and y coordinates for selected values of t. For example, when t = 0, x(0) = 2(0) - 1 = -1 and y(0) = 2\sqrt{0} = 0. Repeat for other values of t like 1, 2, 3, etc.
4. Plot the calculated points (x, y) on the coordinate plane. For instance, plot (-1, 0), (1, 2), (3, 2.83), etc., based on your calculations.
5. Draw a smooth curve through the plotted points and indicate the orientation of the curve by drawing arrows in the direction of increasing t, which is from left to right in this case.