Questions: Fill in the blank to correctly complete the following sentence. The graph of the function f(x) = (x-16)^2 is obtained by shifting the graph of y = x^2 16 units.

Fill in the blank to correctly complete the following sentence. The graph of the function f(x) = (x-16)^2 is obtained by shifting the graph of y = x^2 16 units.

Transcript text: Fill in the blank to correctly complete the following sentence. The graph of the function $f(x)=(x-16)^{2}$ is obtained by shifting the graph of $y=x^{2}$ $\square$ 16 units.

Solution

Solution Steps

To determine how the graph of $ f(x) = (x-16)^2 $ is obtained from the graph of $ y = x^2 $, we need to identify the transformation applied to the basic quadratic function. The function $ f(x) = (x-16)^2 $ represents a horizontal shift of the graph of $ y = x^2 $. Specifically, the graph is shifted to the right by 16 units.

Step 1: Identify the Original Function

The original function is given by $ y = x^2 $. This is the standard form of a quadratic function, which opens upwards and has its vertex at the origin $ (0, 0) $.

Step 2: Analyze the Transformed Function

The transformed function is $ f(x) = (x - 16)^2 $. This represents a horizontal shift of the original function. The expression $ (x - 16) $ indicates that the graph is shifted to the right by 16 units.

Step 3: State the Transformation

Thus, the graph of the function $ f(x) = (x - 16)^2 $ is obtained by shifting the graph of $ y = x^2 $ to the right by 16 units.