2Plotting graphs of quadratic functions y = ax2 + bx + c (where a ≠ 0)A quadratic function in x can be written in the form:We can plot the graph of a quadratic function using a table of values. For example:Plot the graph of y = x2 – 4x + 2 for –1 < x < 5.xx2– 4x+ 2y = x2 – 4x + 2–11234511491625Talk through the substitution for each value of x to give the corresponding value of y.Ask students if they can tell you between which values of x the roots will be.+ 4+ 0– 4– 8– 12– 16– 20+ 2+ 2+ 2+ 2+ 2+ 2+ 272–1–2–127
3Plotting graphs of quadratic functions x–1123457–2y = x2 – 4x + 2The points given in the table are plotted …y6… and the points are then joined together with a smooth curve.543The shape of this curve is called a parabola.Point out that, at this level, graphs are rarely plotted in this way but are usually sketched to show their shape relative to the x- and y-axes and their general features.When a sketch is required we only find the coordinates of the points where the function crosses the axes and the coordinates of any turning points.21It is characteristic of a quadratic function.–112345x–1
4Parabolas Parabolas have a vertical axis of symmetry … …and a turning point called the vertex.When the coefficient of x2 is positive the vertex is a minimum point and the graph is -shaped.When the coefficient of x2 is negative the vertex is a maximum point and the graph is -shaped.
5Graphs of the form y = ax2 + bx + c Change the values of a, b and c to observe how each one affects the shape and position of the parabola.In particular, draw students’ attention to the fact that when a is positive the parabola is -shaped and when a is negative the parabola is -shaped. Changing the value of a stretches or squeezes the graph.Note, too, that when a = 0 the function is no longer quadratic but linear.