Question

The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x) = x²?

Answer 1

Translation of a function y = h(x) to the right/left is given by y = h(x + a)  for translation to the left by 'a' units and y = h(x - a) for translation to the right by 'a' units

Translation of a function y = h(x) up/down the y-axis is given by y = h(x) + a for translation 'a' unit up and y = h(x) - a for translation 'a' unit down

So, translating f(x) = x² eight units right and two units up gives:

g(x) = (x-8)² + 2