Using Calculators to Sketch Graphs (Cambridge (CIE) IGCSE International Maths)

Revision Note

Using Calculators to Sketch Graphs

How do I draw graphs on my graphic display calculator?

  • Navigate on your calculator to the Add Graphs button

    • You may need to start a new document first

    • On some models you will need to select graph mode in the menu

  • Enter the equation of the function on the line f(x)=

    • This is the function, straight f open parentheses x close parentheses

    • On other models it may be labelled as f1(x)= or Y1:

  • Press enter or EXE and the graph should appear

    • You may need to go to the menu or press the zoom button to zoom in or out

      • The "zoom - fit" button (or equivalent) automatically zooms for you on the key features

      • Other models may also have a "V-Window" menu where you can select the exact range of values to show

Examples of linear, quadratic, cubic, reciprocal, and exponential graphs

How do I find graph features using my graphic display calculator?

  • Once the graph is drawn, go to the menu and select analyze graph (or equivalent), which gives a list of options

    • Other models may feature a G-Solv button

  • Zeros (or roots): these are the x-intercepts

    • You may have to click before and after the x-intercept you require so that the calculator knows where to search

    • y-intercepts can be found without a calculator by substituting x equals 0 into straight f open parentheses x close parentheses

      • though some models do include a Y-ICEPT button which can be used

  • Maximum or minimum points: these are the coordinates of the highest point and lowest point on the graph

    • You may have to click before and after the point you require so that the calculator knows where to search

    • These can be called local maxima or local minima

    • They are also referred to as turning points

      • or the vertex if talking about a quadratic graph

positive and negative quadratics with maximum and minimum points labelled respectively
positive cubic with turning points, roots, y intercept, all labelled

How do I sketch a graph in the exam from my graphic display calculator?

  • Exam questions may ask you to sketch the graph on a given blank set of axes

    • You do not need to plot points exactly

      • and you do not need a table of values

    • Drawsingle smooth freehand curve that copies the shape of the curve on your graphic display calculator

      • Do not use a ruler for curves!

      • Copy any key features and symmetries

Quadratic graph with roots, turning point, and y-intercept labelled
  • Exam questions may ask you to use your calculator to sketch an unknown function that you have not seen before

Graphs of y=x^(1/2) and y=x^(-1/2)

How do I create a table of values on my graphic display calculator?

  • Your calculator can create tables of values for you, if needed

  • Find the table function

    • Type in the graph equation (the function, f(x)=) 

    • Enter the start value (or equivalent)

      • The first x-value in the table

    • Enter the end value (or equivalent)

      • The last x-value in the table

    • Enter the step size (or equivalent)

      • How big the steps (gaps) are from one x-value to the next

    • You may have to select SET to set the above values

    • Press enter or EXE to see the table of values

Examiner Tips and Tricks

  • Exam questions will say "draw this graph on your calculator" to make it clear when using a calculator is intended

Worked Example

(a) Draw the graph of y equals 2 x squared minus 4 x minus 6 on your calculator and use it to sketch the curve on the axes provided, showing coordinates of all axes intercepts and any maximum or minimum points.

Start a new graph on your calculator and enter straight f open parentheses x close parentheses equals 2 x squared minus 4 x minus 6 to generate the graph
This shows the curve has a minimum point (not a maximum point)

Select the option to "analyze" the graph (this may be labelled as G-Solv)
Choose the option "zeros" (or roots) to find the x-intercepts
Choose the option "minimum" (or equivalent) to find the coordinates of the minimum point

The question asks for all axes intercepts, so this includes the y-intercept
Substitute x equals 0 into straight f open parentheses x close parentheses equals 2 x squared minus 4 x minus 6 to get -6
(or you can use the Y-ICEPT button on some models)

Show all the above information on a sketch using coordinates

graph of y=2x^2 - 4x -6 showing roots at (-1,0) and (3,0), y intercept at (0,-6), and minimum point at (1,-8)

(b) Match the following curve equations to the sketches below. You may use your graphic display calculator in this question.

(1) y equals 0.6 x plus 2    (2) y equals 3 to the power of x    (3) y equals negative 0.7 x cubed    (4)  y equals 4 over x   (5) y equals negative x squared plus 3 x plus 2

5 different shapes of graph; exponential, reciprocal, negative quadratic, linear, and negative cubic

(1) is a straight line equation (ymx c) so must match graph D

(2) requires plotting on a graphic display calculator to see that it is A

(3) requires plotting on a graphic display calculator to see that it is E

(4) requires plotting on a graphic display calculator to see that it is B

(5) is a quadratic equation with a negative coefficient so matches graph C

When plotting these graphs on your calculator, you may need to use the zoom function or V-Window button to see the overall shapes of the graphs

(1) → D
(2) → A
(3) → E
(4) → B
(5) → C

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Mark Curtis

Author: Mark Curtis

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

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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.