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?
How many different ways do you know to write the equation of a quadratic?
Which of these might be most useful for each of these problems?
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 \(A\)?
Which form of quadratic most easily allows you to find the vertex of the quadratic?
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.
It will be useful when working on this one to use clear notation for the coordinates of \(A\), \(B\) and \(C\). Something like \(A(a_1,a_2)\), \(B(b_1,b_2)\) and \(C(c_1,c_2)\) would work well.