5.
Translations 3
Let's
now look at the translation of functions in any direction.
This can be accomplished through the use of horizontal and vertical components
as vectors, i.e. through a combination of horizontal and vertical
translations, in any order.
|
In the applet, click on the p and q sliders to see how
the graph of y
– p = (x
– q)2 can be moved at an angle by combining
horizontal and vertical translations.
Move
the graph so that the vertex is at the point (3, 4),
then (-3, 4), then (-3, -4), then …
Describe
the relationship between the movements and the parameters
p and q and the corresponding equation.
Click "init" to reset, change the
value of n and investigate the translation of the function
as you change p and q ... |
|
|
|
|
|
Here
is another applet for you to reflect on horizontal and vertical
translations.
Select the functions from the drop-down menu, or enter your
own functions. Observe how different translations move the
graph, and note the corresponding algebraic formula.
Formulate
the relationships.
|
|
|
Open
the Excel circle worksheet. Click on the sliders to see how
the graph of (x
– h)2 + (y
– k)2 = 4 can be moved at an angle by combining
horizontal and vertical translations.
Move
the purple circle so that its centre is at the point (3, 4),
then (-3, 4), then (-3, -4), then …
Describe
the relationship between the movements and the parameters
h and k.
|
|
| |
Move
your mouse over this picture of Mickey Mouse ...
Your challenge is to draw Mickey!
Click
on the picture to open the Mickey Mouse applet.
Note: In the applet, type in (replace) the values
of h, k and r in the equations of the missing circles
and press ENTER. If your circle is not correct, try
again ...
|
|
|
|
|