To help students understand the links between algebraic and graphical representations technology can be so helpful. Try Graphing Quadratics from PhET Interactive Simulations. Using this you can generate definitions for vertex, roots, axis of symmetry and compare different forms of a quadratic function. For your older students, you can define a curve by its focus and directrix!

PhET Graphing Quadratics

Focus & Directrix

These interactive simulations work on phones and tablets as well as desktops.

We could also use Desmos, GeoGebra or WolframAlpha to quickly demonstrate a graphical representation.

For an excellent teaching resource for looking at multiple representations of quadratics, try Pick a Card from Underground Mathematics.

Underground Mathematics – Pick a Card

Each of the cards in this interactivity describes the same quadratic function. If you reveal one card (by clicking it), can you work out the content of all the other cards? Some questions to consider and more details about the interactivity are also given.

As with all Underground Mathematics resources, teacher notes and supporting materials are provided.

See Malcolm Swan’s wonderful Improving Learning In Mathematics for commentary on using multiple representations (See section 4.2). This publication discusses effective teaching so well to help us think about just what makes a quality resource for learning.

Improving Learning In Mathematics is part of The Standards Unit. (The link takes you to a page where you can access all the Standards Unit resources.)

Nrich has many articles and tasks which encourage students to explore multiple representations.