Question

Describe in words the transformation of the graph of the parent function f(x) = x^2 that would result in the graph of g(x) = (x+4)^2 - 5. Which of the following describes this transformation?

A) The graph of g is a translation of the graph of f, 4 units to the right and 5 units down.
B) The graph of g is a translation of the graph of f, 4 units to the left and 5 units up.
C) The graph of g is a translation of the graph of f, 4 units to the left and 5 units down.
D) The graph of g is a translation of the graph of f, 4 units to the right and 5 units up.

Answer 1

The graph of g(x) = (x+4)^2 - 5 is a translation of the graph of the parent function f(x) = x^2. The correct transformation is a shift 4 units to the left and 5 units up.

Step-by-step explanation:

The graph of g(x) = (x+4)^2 - 5 is a translation of the graph of the parent function f(x) = x^2. To describe this transformation, we can note that the graph of g is obtained by shifting the graph of f 4 units to the left and 5 units down.

Therefore, the correct answer is B) The graph of g is a translation of the graph of f, 4 units to the left and 5 units up.