Package of problems

## Suggestion

### 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.