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

Dan Finlay

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

Why do I need to solve equations graphically?

  • Some equations cannot be solved analytically

    • 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 might 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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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.