4. On a plane, $n$ points with distinct abscissas are marked. Through each pair of points, a parabola, the graph of a quadratic trinomial with a leading coefficient of one, is drawn. A parabola is called good if there are no marked points on it or above it, except for the two points through which it is drawn. What is the maximum number of good parabolas that could result?
Answer: $n-1$ parabolas. Example: parabolas passing through $n$ points on the X-axis. Evaluation: connect two marked points with an edge if the parabola passing through them is good. Suppose that two good parabolas pass through a given point $A$. To the right of point $A$, one of the parabolas lies above the other, so it cannot be the case that the second marked points on each of the two parabolas are to the right of $A$. Therefore, from each point, there can be at most two edges - one to the right, and one (for similar reasons) to the left. Moreover, from the leftmost and rightmost points, there can be at most one edge. Therefore, there are no more than $n-1$ edges, i.e., no more than $n-1$ good parabolas.