Question

Explain how you would graph the following set of parametric equations by plotting points and describing the orientation.

X = 3t and y = t^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To graph the set of parametric equations X = 3t and y = t^2, we can plug in different values of t to generate points.

When t = 0, X = 3(0) = 0 and y = (0)^2 = 0. So the point (0,0) is on the graph.

For t = 1, X = 3(1) = 3 and y = (1)^2 = 1. So the point (3,1) is on the graph.

Similarly, for t = -1, X = 3(-1) = -3 and y = (-1)^2 = 1. So the point (-3,1) is also on the graph.

By connecting these points, we can see that the graph is a parabola opening upwards, with the vertex at (0,0) and the axis of symmetry along the y-axis. The orientation of the graph is determined by the direction in which t is increasing, which in this case is to the right.