Drawing Graphs from Tables (Edexcel IGCSE Maths A (Modular))

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Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

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Drawing Graphs Using a Table

How do I draw a graph using a table of values?

  • To create a table of values

    • substitute different x-values into the equation

      • This gives the y-values

  • To plot the points

    • use the and y-values to mark crosses on the grid at the coordinates (x , y )

      • Each point is expected to be plotted to an accuracy within half of the smallest square on the grid

  • Drawsingle smooth freehand curve 

    • Go through all the plotted points

    • Make it the shape you would expect

      • For example, quadratic curves have a vertical line of symmetry

    • Do not use a ruler for curves!

Which numbers should I be careful with?

  • For quadratic graphs, be careful substituting in negative numbers 

    • Always put brackets around negative values and use BIDMAS

      • For example, substitute x = -3 into y = -x2 + 8x 

      • This becomes y = -(-3)2 + 8(-3)

      • which simplifies to -9 - 24

      • so y = - 33

  • For reciprocal graphs like y equals 1 over x, or y equals 1 over x squared, do not include = 0

    • You cannot divide by zero

      • You get an error on your calculator

    • There is no value at x = 0 

      • The L-shaped branches can't cross the y-axis

      • There will be a vertical asymptote at x = 0

    • An example is given below with y equals 1 over x

x

-3

-2

-1

0

1

2

3

y

negative 1 third

negative 1 half

negative 1

No value

1

1 half

1 third

  • You should also be careful when there is a combination of different types of function

    • E.g. y equals x squared minus 1 over x plus 4 has a quadratic term and a reciprocal term

    • This makes it harder to know the shape of the graph

    • But you can still use a table of values to plot them

    • Just be aware of points like x = 0 as described above, where there will be no value

How do I use the table function on my calculator?

  • Calculators can create tables of values for you

  • Find the table function

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

      • Use the alpha button then X or x

      • Press = when finished

    • If you are asked for another function, g(x), press = to ignore it

  • Enter the start value

    • The first x-value in the table

    • Press =

  • Enter the end value

    • The last x-value in the table

  • Enter the step size

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

    • Press =

  • Then scroll up and down to see all the y-values

Examiner Tips and Tricks

  • If you find a point that doesn't seem to fit the shape of the curve, check your working!

  • If any y-values are given in the question, check that your calculations agrees with them

Worked Example

(a) Complete the table of values for the graph of y equals 10 minus 8 x squared.

x

negative 1.5

negative 1

negative 0.5

0

0.5

1

1.5

y

 

2

 

 

 

 

negative 8

Use the table function on your calculator for straight f open parentheses x close parentheses equals 10 minus 8 x squared
Start at -1.5, end at 1.5 and use steps of 0.5

Alternatively, substitute the x-values into the equation, for example x = -1.5

table row y equals cell 10 minus 8 open parentheses negative 1.5 close parentheses squared end cell row blank equals cell 10 minus 8 cross times 2.25 end cell row blank equals cell 10 minus 18 end cell row blank equals cell negative 8 end cell end table

x

negative 1.5

negative 1

negative 0.5

0

0.5

1

1.5

y

-8

2

8

10

8

2

negative 8

(b) Plot the graph of y equals 10 minus 8 x squared on the axes below, for values of x from negative 1.5 to 1.5.

Carefully plot the points from your table on to the grid
Note the different scales on the axes

Join the points with a smooth curve (do not use a ruler)

graph of the table of values for a negative quadratic

(c) Write down the equation of the line of symmetry of the curve.

There is a vertical line of symmetry about the y-axis

The equation of the y-axis is x = 0

x = 0

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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.

Dan Finlay

Author: Dan Finlay

Expertise: Maths 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.