f(x) = (x - 5)² + 7
Translations are transformations that change the position of the graph of a function. The general shape of the graph of a function translates up, down, to the right, or to the left.
Vertical translations:
Let k > 0:
To graph y = f (x) + k, shift the graph up k units.
To graph y = f (x) -k, shift the graph of k units down.
Horizontal translations:
Let w>0
To graph y = f (x-w), shift the graph w units to the right.
To graph y = f (x + w), shift the graph w units to the left.
Let:
f(x) = x²
Shift f(x) 7 units up:
f(x) = x² + 7
And shift f(x) 5 units to the right:
f(x) = (x - 5)² + 7