Harold argues that a semi-circle has rotation symmetry, but Jay disagrees. Who is correct and why?

See below.

Step-by-step explanation:

Jay is correct.

If you draw a semicircle with a diameter and use the center of the circle as the point of rotation, the figure will only look the same as the original when it is rotated 360 degrees. This gives the semicircle an order of rotation of 1. That means that once you start rotating a semicircle, it only looks like itself after a full 360-degree rotation. It does not have rotational symmetry.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.