Drawing Graphs from Tables (Edexcel GCSE Maths)

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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 x 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
Draw a single 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 $y = \frac{1}{x}$ , or $y = \frac{1}{x^{2}}$ , do not include x = 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 $y = \frac{1}{x}$

$x$	-3	-2	-1	0	1	2	3
$y$	$- \frac{1}{3}$	$- \frac{1}{2}$	$- 1$	No value	$1$	$\frac{1}{2}$	$\frac{1}{3}$

You should also be careful when there is a combination of different types of function
- E.g. $y = x^{2} - \frac{1}{x} + 4$ 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 $y = 10 - 8 x^{2}$ .

$x$	$- 1.5$	$- 1$	$- 0.5$	$0$	$0.5$	$1$	$1.5$
$y$		$2$					$- 8$

Use the table function on your calculator for $f (x) = 10 - 8 x^{2}$
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

$\begin{array}{rcl} y & = & 10 - 8 {(- 1.5)}^{2} \\ = & 10 - 8 \times 2.25 \\ = & 10 - 18 \\ = & - 8 \end{array}$

$x$	$- 1.5$	$- 1$	$- 0.5$	$0$	$0.5$	$1$	$1.5$
$y$	-8	$2$	8	10	8	2	$- 8$

(b) Plot the graph of $y = 10 - 8 x^{2}$ on the axes below, for values of $x$ from $- 1.5$ 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

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

The equation of the y-axis is x = 0

x = 0

Last updated: 17 October 2024

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