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IBMathsDPAnalysis & Approaches (AA)SLRevision Notes2. FunctionsFurther Functions & GraphsSolving Equations Graphically

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

Dan Finlay

Author

Last updated

5 June 2025

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Solving Equations Graphically

How can I solve equations graphically?

To solve $f (x) = g (x)$
- One method is to draw the graphs $y = f (x)$ and $y = g (x)$
  - The solutions are the x-coordinates of the points of intersection
- Another method is to draw the graph $y = f (x) - g (x)$ or $y = g (x) - f (x)$
  - 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
  - $x^{5} - x + 1 = 0$
- Equations involving different types of functions
  - $e^{x} = x^{2}$

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 $y = e^{x} - x^{2}$ .

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

b) Hence find the solution to $e^{x} = x^{2}$ .

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.