Question

In what direction, and how far, must f(x) = x² be shifted so that it coincides with f(x) = (x - 6)²?

Answer 1

To make f(x) = x² coincide with f(x) = (x - 6)², the graph of f(x) = x² must be shifted 6 units to the right along the x-axis.

Step-by-step explanation:

The student's question relates to shifting the graph of a quadratic function. Specifically, the student is asking in what direction, and how far, the function f(x) = x² must be shifted to coincide with f(x) = (x - 6)². To make these two functions coincide, the graph of f(x) = x² needs to be shifted 6 units to the right along the x-axis. This is because the function f(x) = (x - 6)² represents a horizontal translation of f(x) = x², where the entire graph is moved 6 units to the right without changing its shape.