### Two points on the axis

Using GeoGebra, plot two points \(A\) and \(B\) on the \(x\)-axis of a graph. Can you instruct GeoGebra to draw a quadratic which passes through both of them?

*It should be constructed in such a way that when you move either \(A\) or \(B\) along the \(x\)-axis, the quadratic changes so that it continues to pass through both of them.*

*If you want some guidance on how to get the coordinates of the points \(A\) and \(B\), or how to enter an equation in GeoGebra, see the Using GeoGebra section.*

This applet shows what the result could look like:

### One point as the vertex

On a new graph, plot a point \(A\). Can you instruct GeoGebra to draw a quadratic which has its vertex at \(A\)?

*It should be constructed in such a way that when you move \(A\), the quadratic changes in response.*

This is what the result could look like:

### Any three points

The final (very hard) challenge: plot three points \(A\), \(B\) and \(C\) anywhere on the graph, and draw a quadratic passing through these three points, like this:

Is there more than one quadratic you could draw?