Which method we use to graph a parabola depends on the form of the equation we are given. For example, if the function is given in "general" form, i.e. y = ax² + bx + c, it is generally simplest to find the vertex of the parabola, its y-intercept, and then to determine whether the parabola opens up or down. Once we know these facts, graphing the parabola is a straightforward matter.

You can see an example of this process worked out step by step.

Another option in graphing a parabola is to use the shifting and scaling techniques we have seen in Graphing Techniques . In order to do this, the function must be given in standard form, i.e. y = a(x - h)² + k. If it is not given in this form, you may use the technique of completing the square to bring the function to standard form. Once it is in this form, remember that the vertex is at the point (h, k), and scale the graph using a.

In the next activity you may practice graphing parabolas using both methods. In order to begin (or get a new exercise once you've begun), click on the "New" button. The applet will guide you through the steps: entering the vertex, the y-intercept, and the x-intercept/s (if there are any). At any stage of your work here you may click on "Help" to find out what to do, or on "Solve" if you want to see the full solution (for that stage).

Notice that you click on the appropriate points on the plane to enter the vertex and y-intercept, but you type in the x-intercepts in the work space in the middle on the bottom. Don't forget to click in that space first to activate it!

Also notice that you may get help or solutions on either method by choosing the appropriate buttons: VF for vertex formula, and CS for completing the square.

Graphing Parabolas