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Learning objective

Identify, draw, and analyze graphs of various functions including linear, quadratic, cubic, reciprocal, and exponential functions. This includes understanding turning points, roots, and symmetry, as well as recognizing vertical and horizontal asymptotes. You should be able to find turning points of quadratic functions by completing the square.

Read the explanation, check the common trap, then practise with flashcards and questions.

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  • Read the explanation.
  • Check key terms.
  • Practise with linked questions.
Cambridge IGCSE MathematicsExtended Algebra and graphsSupplement content

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Quick explanation

Identify, draw, and analyze graphs of various functions including linear, quadratic, cubic, reciprocal, and exponential functions. This includes understanding turning points, roots, and symmetry, as well as recognizing vertical and horizontal asymptotes. You should be able to find turning points of quadratic functions by completing the square

  • This point belongs to Sketching curves, especially Sketching curves outcomes.
  • You need to be able to identify, draw, and analyze graphs of various functions including linear, quadratic, cubic, reciprocal, and exponential functions. This includes understanding turning points, roots, and symmetry, as well as recognizing vertical and horizontal asymptotes. You should be able to find turning points of quadratic functions by completing the square.
  • The key ideas to know are Sketch, Show, and Describe.
  • Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.

Key concepts

SketchShowDescribeDetermine

Why it matters

This objective helps connect Sketching curves outcomes to exam-style questions, flashcards, and revision notes for Sketching curves.

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Practice Questions7 linked questions

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Paper 2 structured question: Sketching curves

Paper 2Core or Extended Mathematics3 marks

Description

Quadratic Function Graph

Consider the quadratic function y = x^2 - 4x + 3.

  1. a

    Calculate the coordinates of the turning point by completing the square.

    Aim for approximately 3 distinct marking points.

    [3]
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