Full Quadratic Functions Notes — Cambridge IGCSE Additional Mathematics 0606

Topic 2: Quadratic functions. Built from the 2025–2027 Cambridge IGCSE Additional Mathematics 0606 syllabus.

What this chapter must train

By the end, students should be able to:

• Find the maximum or minimum value of a quadratic function.
• Complete the square.
• Use differentiation to find the turning point when useful.
• Sketch quadratic graphs.
• Determine range for a given domain.
• Use the discriminant to decide the nature of roots.
• Understand when a line intersects, touches, or misses a quadratic curve.
• Solve quadratic equations.
• Solve quadratic inequalities graphically or algebraically.

1. What a quadratic function is

A quadratic function has the form:

$$ f(x)=ax^2+bx+c, \quad a\ne 0 $$

The graph of a quadratic is a parabola.

• If (a>0), the parabola opens upwards.
• If (a<0), the parabola opens downwards.