The vertex form of the quadratic equation is f(x) = a(x - h)² + k and the standard form is f(x) = a x² + b x + c.
Adjust the sliders a, h, and k to create the quadratic equation that you wish to explore. The vertex is at (h, k). Select check box to set the vertex
Select check box to see roots or points of intersection of the graph and the x-axis. Another check box will show how to use the quadratic formula to solve for the roots of the equation.

The check boxes are for three points that are selected on the graph. These points will allow the exploration of points on the graph by selecting box A, B, or C. Use these points to solve for the quadratic formula on the right using y = a x² + b x + c by solving the system of equations. Select the check boxes with the move arrow to see the actual coordinates. By selecting the point you can move the points with the mouse or the keyboard cursor keys.
This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers with a worksheet to be complete for a grade.