The graph of a quadratic function is a parabola.
Here are some examples:
Experiment with the applet below, varying the value of a in the quadratic equation y = ax2 to see how changing a changes the graph. The initial graph shown is y = x2 and remains stationary for comparison.
Note that the parabola given by y = ax2 opens up (concave upward) if a > 0 and it opens down (concave downward) if a < 0.
Each parabola is symmetric about a vertical line called the axis which passes through a point called the vertex. In the parabola y = ax2, the vertex is the origin.
Now we look at examples of how to draw the graph of a quadratic function. We do this by first finding the vertex through which the axis can be drawn.
When using the applet, enter the function you wish to be drawn on the function line and click on new function. The applet starts with f(x) = x^2 + 2x + 1. To look at a particular point on the graph (the vertex for example) enter the value of x in the box provided and the point will be highlighted by a grey '+'.
Now try a few on your own.