Is the particle ever moving straight horizontally right or

Question

Question: For x and y in meters, the motion of the particle given by

x = t³ - 3t, y = t² - 2t

Where the y-axis is vertical and the x-axis is horizontal.

(a) Does the particle ever come to a stop? If so, when and where?

(b) Is the particle ever moving straight up or down? If so, when and where?

(c) Is the particle ever moving straight horizontally right or left? If so, when and where?