If your original function is y = x²
and you want to translate it 3 units to the right, replace x with x - 3: y = (x - 3)².
If you want ot translate it 5 units to the left, replace x with x + 5: y = (x + 3)².
Notice, if you want to move it to the right, use a - sign; to the left, use a + sign.
If you want to translate it 4 units up, replace y with y - 4: y - 4 = x²
(or y = x² + 4).
If you wnat to translate it 7 units down, replace y with y + 7: y + 7 = x²
(or y = x² - 7).
A translation of the vertex from (0, 0) to (a, b) results in the equation: y - b = (x - a)².