The translation of the given graph has done in two steps.
1. Horizontal shift of 5 units to the left
2. Vertical shift of 4 units in the downwards direction.
"The translation of a graph is its rigid movement, vertically or horizontally."
The given translation of graph is:
[tex]y = (x - 6)^{2} + 7[/tex] to [tex]y = (x - 1)^{2} + 3[/tex]
Here, two types of translation has done to the first graph.
1. First of all, there is a horizontal shift of 5 units to the left has done.
[tex]y = (x - 6)^{2}[/tex] ⇒ [tex]y = [(x - 1) - 5)]^{2}[/tex]
2.After that, there is a vertical shift of 4 units in the downwards direction.
[tex]y = (x - 6)^{2} + 7[/tex] ⇒ [tex]y = (x - 1)^{2} + 3[/tex]
Learn more about the translation of a graph here: https://brainly.com/question/12982455
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