Draw a quadratic curve - the simplest one's just y = x². Pick two coordinates, one either side of the y-axis. It's most satisfying if you pick integer points, but works with any (x,y) coordinate pair. Then draw a line segment from one point to another.
From this we get a couple of nice little results:
While not particularly groundbreaking (or, as far as I can work out, useful?), it would make a fantastic quick investigation for Higher GCSE pupils, and in particular offer lots of practice finding the gradient of a line joining two points.
(Graph created using Desmos, annotations my own)