# Equations and Expressions: Level 5

The key idea of equations and expressions at level 5 is that some types of relationships between variables can be represented by a quadratic equation.

Quadratic equations take the form:
y = ax2 + bx + c.
where x represents a variable, and a, b, and c, constants, and a is not 0 (if a is 0 the equation is a linear equation).  The graph of a quadratic equation is a parabola.  Quadratic equations are useful in modelling a variety of real-world situations, with one of the most common examples being projectile motion – the path taken by an object through the air forms a parabola.

At level 5 students will be exploring simple quadratic equations, in the form y = ax2 or y = x2 + c,  where a and c are integers.   Students at this level should be able to operate on quadratic equations by applying inverse operations.   They will also recognise where it is appropriate to solve an equation through trial and improvement, and find missing values by systematic calculation.  At higher levels quadratic equations can be solved by factorising, by completing the square, by graphing, or by using the quadratic formula.

This key idea develops from the key idea of equations and expressions at level 4 where students explore relationships between variables which can be represented by a linear equation.

This key idea links to the key idea of patterns and relationships at level 5.

This key idea is extended to the key idea of equations and expressions at level 6 where more complex expressions such as linear inequations, exponential equations, and simultaneous equations are introduced.