### Why use this resource?

This resource prompts students to think about what information is needed to be able to identify an equation for a parabola directly from the graph.

### Possible approach

Students should be encouraged to think about the three ‘forms’ of a quadratic equation that they may be familiar with: expanded form \((y=ax^2+bx+c)\), fully factorised form \((y=a(x-d)(x-e))\); and completed square form \((y=a(x-f)^2+g)\). They should continually reflect on the efficiency of their approach and whether they can be applied to a general parabola.

It is nice to highlight transformations of graphs as an effective approach for the blue parabola in this problem.

### Key questions

Which approach to finding the equation was the most efficient? Is it the same approach for each example?

### Possible support

Students could use Desmos (a graphing calculator) to check their solutions.

### Possible extension

Which of these approaches would work best for cubic polynomials? Explain your thinking. Can any of these approaches be generalised for other polynomials.

A version of this resource has been featured on the NRICH website.