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Solving Equations Graphically (DP IB Analysis & Approaches (AA)): Revision Note

Dan Finlay

Written by: Dan Finlay

Reviewed by: Lucy Kirkham

Updated on

DP Analysis & Approaches (AA): SLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): HL

Solving equations graphically

How can I solve equations graphically?

  • To solve space f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis

    • One method is to draw the graphs space y equals f left parenthesis x right parenthesis and space y equals g left parenthesis x right parenthesis

      • The solutions are the x-coordinates of the points of intersection

    • Another method is to draw the graph space y equals f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis or space y equals g left parenthesis x right parenthesis minus f left parenthesis x right parenthesis

      • The solutions are the roots (zeros) of this graph

      • e.g. the solutions to x cubed equals 5 straight e to the power of x are the roots of the graph y equals x cubed minus 5 straight e to the power of x

Why do I need to solve equations graphically?

  • Some equations cannot be solved analytically

    • Most polynomials of degree higher than 4

      • x to the power of 5 minus x plus 1 equals 0

    • Equations involving different types of functions

      • straight e to the power of x equals x squared

Examiner Tips and Tricks

On a calculator paper you are allowed to solve equations using your GDC unless the question asks for an algebraic method.

If your answer needs to be an exact value then you need to solve analytically to get the exact value.

Worked Example

a) Sketch the graph y equals straight e to the power of x minus x squared.

2-4-3-ib-aa-sl-solve-graphically-a-we-solution

b) Hence find the solution to straight e to the power of x equals x squared.

2-4-3-ib-aa-sl-solve-graphically-b-we-solution

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    Author
    Reviewer
    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

    Lucy Kirkham

    Reviewer: Lucy Kirkham

    Expertise: Head of Content Creation

    Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels.Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all.