Drawing Graphs from Tables (Edexcel IGCSE Maths)

Drawing Graphs Using a Table

Spec point — 3.3I

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 curved branches can't cross the y-axis **
    • There will be a** vertical asymptote at x = 0

  • An example is given below with $y=\frac{1}{x}$

• 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

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

Worked Example (a) Complete the table of values for the graph of $y=10-8x^{2}$.

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

Answer:

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

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

$x$	$-1.5$	$-1$	$-0.5$	$0$	$0.5$	$1$	$1.5$
$y$	Final answer: -8	$2$	Final answer: 8	Final answer: 10	Final answer: 8	Final answer: 2	$-8$

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

Answer:

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)

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

Answer:

The curve is symmetrical about the y-axis

The equation of the y-axis is x = 0

Final answer: x = 0