It is often not necessary to plot quadratics by drawing up a table of x values and corresponding y values. Often a few points will suffice to obtain the main features of the graph and sketch it. The main features of a quadratic graph are:

The vertex. This is the maximum or minimum of the graph. A quadratic has eithe a maximum or a minimum, and there is only one of them. If the equation of the graph is and then the vertex is a maximum and the coordinates of the vertex are  The graph above left has a vertex at This is a maximum because The graph above right has a vertex at The equation of the line of symmetry. For a quadratic graph the equation of the line of symmetry is For (above left), this gives The – intercept. This is easily found by substituting in the equation of the graph For we obtain The - intercept(s), if they exist. Not every quadratic has - intercepts. For intercepts to exist, the equation must have real solutions. Since the solutions are given by we must have that: for a unique solution. The graph touches the – axis but does not cross it. for two distinct solutions. In this case the two solutions are given by and The - intercepts for the graph are and If the quadratic factorises then we may find the intercepts by setting each factor equal to 0. For example factorises as and   