IGCSE Quadratic Functions: Complete Guide for Cambridge IGCSE Mathematics

IGCSE quadratic functions are essential function topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering quadratic function properties, vertex form, and completing the square is essential for understanding parabolas and their applications.

This comprehensive IGCSE quadratic functions guide covers everything you need to know, including standard form, vertex form, axis of symmetry, maximum/minimum values, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to identify quadratic function properties, find vertex and axis of symmetry, convert between forms, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Quadratic Functions Matter

IGCSE quadratic functions are essential function topics. Here’s why they’re so important:

• High frequency topic: Quadratic function questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for understanding parabolas and optimization
• Exam weight: Typically worth 6-10 marks per paper
• Real-world applications: Used in physics, engineering, and optimization problems
• Problem-solving skills: Develops understanding of function behavior and graphs

Key insight from examiners: Students often struggle with completing the square or finding the vertex. This guide will help you master these systematically.

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Understanding Quadratic Functions

Quadratic function: f(x) = ax² + bx + c where a ≠ 0

The graph is a parabola.

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Standard Form

Standard form: f(x) = ax² + bx + c

Properties:

• If a > 0: Parabola opens upward (minimum point)
• If a < 0: Parabola opens downward (maximum point)
• Axis of symmetry: x = -b/(2a)
• Vertex: (-b/(2a), f(-b/(2a)))

Example 1: Find the vertex of f(x) = x² - 4x + 3

Solution: a = 1, b = -4, c = 3 Axis of symmetry: x = -(-4)/(2×1) = 2 f(2) = 4 - 8 + 3 = -1 Vertex: (2, -1)

Answer: (2, -1)

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Vertex Form

Vertex form: f(x) = a(x - h)² + k

Properties:

• Vertex: (h, k)
• Axis of symmetry: x = h
• If a > 0: Minimum value is k
• If a < 0: Maximum value is k

Example 2: Write f(x) = x² - 6x + 5 in vertex form

Solution: Complete the square: f(x) = (x² - 6x) + 5 = (x - 3)² - 9 + 5 = (x - 3)² - 4

Answer: f(x) = (x - 3)² - 4, vertex: (3, -4)

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Maximum and Minimum Values

Example 3: Find the maximum value of f(x) = -2x² + 8x - 5

Solution: Since a = -2 < 0, function has a maximum Axis of symmetry: x = -8/(2×-2) = 2 f(2) = -8 + 16 - 5 = 3 Maximum value: 3

Answer: 3

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Common Examiner Traps

• Vertex calculation errors - Use formula x = -b/(2a) correctly
• Completing the square errors - Remember to add and subtract the same value
• Sign errors - Watch positive/negative signs carefully

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Practice Questions

Question 1

Find the vertex of f(x) = 2x² - 8x + 6

Solution: x = -(-8)/(2×2) = 2 f(2) = 8 - 16 + 6 = -2 Vertex: (2, -2)

Answer: (2, -2)

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Frequently Asked Questions About IGCSE Quadratic Functions

What is a quadratic function?

A quadratic function has the form f(x) = ax² + bx + c where a ≠ 0. Its graph is a parabola.

How do I find the vertex?

Use x = -b/(2a) to find the x-coordinate, then substitute to find y-coordinate.

What is vertex form?

Vertex form is f(x) = a(x - h)² + k where (h, k) is the vertex.

How do I find maximum or minimum values?

Find the vertex. If a > 0, it’s a minimum. If a < 0, it’s a maximum.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Quadratic Equations: Complete Guide - Master solving quadratics
• IGCSE Graphs of Functions: Complete Guide - Master function graphs
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Quadratic Functions with Tutopiya

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