Package of problems

# GeoGebra constructions... quadratic edition Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Problem

### 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?