Factored Form of the equation of a parabola is used often, as it is often the easiest way to create the equation of a parabola with two specific roots ([i]x[/i]-intercepts).[br][br]The graph below contains three green sliders. Click on the circle in a slider and drag it to the left or right, while watching the effect it has on the graph.[br][br]The graph will display the coordinates of the points where the graph intersects each axis, as well as the coordinates of the vertex of the parabola.

Once you have a feel for the effect that each slider has, see if you can adjust the sliders so that:[br][br]- the vertex lies to the right, or left, of the [i]y[/i]-axis[br][br]- the vertex lies above the [i]x[/i]-axis[br][br]- the graph becomes a horizontal line[br][br]- some part of the graph passes through the blue point on the graph: (-3, -1)[br][br]- the vertex of the graph (the purple point labelled V) passes through the blue point on the graph: (-3, -1). This is more challenging![br][br][b]a[/b] is referred to as the "dilation factor". It either stretches the parabola away from the [i]x[/i]-axis, or compresses it towards the [i]x[/i]-axis. Note what happens to the graph when you set [b]a[/b] to a negative value. [br][br][b]M[/b] and [b]N[/b] are referred to as the "roots" or the "zeroes" of the function. They determine where the function will cross the [i]x[/i]-axis.[br][br]These three values, [b]a[/b], [b]M[/b], and [b]N[/b], will describe a unique parabola. To completely describe any parabola, all someone needs to tell you are these three values. However, there are also other ways of describing everything about a parabola.[br][br]If you wish to use other applets similar to this, you may find an index of all my applets here: [url=https://mathmaine.wordpress.com/2010/04/27/geogebra/]https://mathmaine.com/2010/04/27/geogebra/[/url]