Question

what value represents the horizontal translation from the graph of the parent function f(x) = x2 to the graph of the function g(x) = (x – 4)2 2?

Answer 1

The graph of the function g(x) = (x - 4)^2 + 2 is 4 units to the right of the function f(x) = x^2.
Hence, the horizontal translation of the function f(x) = x^2 to the function g(x) = (x - 4)^2 + 2 is +4.

Answer 2

In the attached diagram you can see graphs of bpth functions f(x) {red curve} and g(x) {blue curve}. This graphs are the same, but the graph of the function g(x) is obtained from the graph of the function f(x) by translation 4 units right and 2 units up. Translation right is horizontal translation and translation up is vertical translation. Therefore, the value of the horizontal translation is 4.

Answer: 4.