Quadratic functions

Using this applet

In the left pane is a graph of \(y=\text{f}(x)\). On the right, you can click to reveal various features and representations of the function, such as the factorised form (where possible), vertex form, line of symmetry, and more.

You can also move the blue point on the graph to see dynamically resizing algebra tiles, which may be help make things “click” for students, especially if you focus on:

  • how the factorised tiles appear at the roots (where roots exist);
  • how the “completed square” tiles appear at the turning point; and
  • how each of the two representation appears at the -intercept.

You can generate new quadratic functions by clicking the New function button. When launched, the applet only generates monic quadratics with integer roots. By clicking the Options▼ dropdown, you can allow the applet to also generate non-monics, quadratics with irrational roots, and quadratics with no roots.

This applet has been partly inspired this tweet from Ashley McGuire, whose website is makeemthinkmaths.com

Putting it all together

This task presents sketches with various points and coefficients marked but not necessarily labelled. The goal is to fill in the blanks.

Download the task