the graph is a curve and should NOT be joined by using straight line.
A note on how to draw the curve "more accurately":
As the graph is a graph for a quadratic eqn, we know that is symmetric. Therefore, by drawing a horizontal line, say at y=50, you can easily locate 2 intersection points with the cruve. Then take the mid point of these 2 intersection point on horizontal line. This is where the max-value of S.
As you know where does the max value occur, then u can draw the curve accordingly (i.e. the curve should reach its max value at the given t value