In functions; translations are used to move lines, points or shapes across the graph (i.e. up, down, right or left).
The translation from [tex]y = (x - 5)^2 +5[/tex] to [tex]y = (x - 0)^2 +0[/tex] is to shift [tex]y = (x - 5)^2 +5[/tex] to the left by 5 units and then downward by 5 units
The given parameters are:
[tex]y = (x - 5)^2 +5[/tex]
[tex]y = (x - 0)^2 +0[/tex]
Assume the first point is: [tex]y = (x - 5)^2 +5[/tex]
While the second is: [tex]y = (x - 0)^2 +0[/tex]
The first point is first shifted left by 5 units
The rule to this translation is: [tex](x,y) \to (x + 5,y)[/tex]
So, we have:
[tex]y' = (x - 5 + 5)^2 + 5[/tex]
[tex]y' = (x - 0)^2 + 5[/tex]
Next, the resulting function is shifted down by 5 units.
The rule to this translation is: [tex](x,y) \to (x,y- 5)[/tex]
So, we have:
[tex]y" = y' - 5[/tex]
This gives:
[tex]y" = (x - 0)^2 + 5 - 5[/tex]
[tex]y" = (x - 0)^2 + 0[/tex]
Hence, the translation from [tex]y = (x - 5)^2 +5[/tex] to [tex]y = (x - 0)^2 +0[/tex] is to shift [tex]y = (x - 5)^2 +5[/tex] to the left by 5 units and then downward by 5 units
Read more about transformations at:
https://brainly.com/question/16619654
