Drawing Parabolas

Drawing parabolas

Parabolas can be drawn relatively easily with the help of a table of values.The following procedure offers an alternative possibility:

1.$$To draw a parabola, it is first necessary to determine the vertex. This is done either by completing the square or via the vertex form

• Draw the vertex in the coordinate system.

2.$$Go from the vertex:

• one length unit to the right or left

• if $a$ is positive: by $|a|$ upwards

  if $a$ is negative: down by $|a|$

3.$$  Go from the vertex:

• two to the right or left

• if $a$ is positive: in $2^2\cdot \left|a\right|=4\cdot \left|a\right|$ upwards

• if $a$ is negative: $4\cdot \left|a\right|$ downwards

4.$$One can continue the scheme for larger distances on the x-axis. It is also possible to choose other step lengths, such as $2$ or $0.5$ to go left or right from the vertex.

• go any distance $\mathrm{\Delta }x$ you consider suitable to the right or left

• if $a$ is positive: go up by $\mathrm{\Delta }{x}^2|a|$

• if $a$ is negative: go down by $\mathrm{\Delta }{x}^2|a|$

5.$$Draw the graph through the plotted points

Example

The following applet shows the procedure for the task:

• Draw the parabola $\begin{array}{l}y=a{(x-2)}^2-1\\ \end{array}$

On the right edge of the applet you will find two sliders. With the first one you can display the steps and with the second one you can change the factor $a$.