Questions: The graph of the function f(x)=(x+15)^2 is obtained by shifting the graph of y=x^2 square 15 units.

Transcript text: The graph of the function $f(x)=(x+15)^{2}$ is obtained by shifting the graph of $y=x^{2}$ $\square$ 15 units.

Solution

Solution Steps

To determine how the graph of $ f(x) = (x + 15)^2 $ is obtained from the graph of $ y = x^2 $, we need to identify the transformation applied to the basic quadratic function. The term $ (x + 15) $ indicates a horizontal shift. Specifically, adding 15 inside the function $ (x + 15) $ shifts the graph to the left by 15 units.

Solution Approach

The graph of the function $ f(x) = (x + 15)^2 $ is obtained by shifting the graph of $ y = x^2 $ left 15 units.

Step 1: Identify the Transformation

The given function is $ f(x) = (x + 15)^2 $. We need to determine how this function is related to the basic function $ y = x^2 $.

Step 2: Understand Horizontal Shifts

The function $ y = (x + c)^2 $ represents a horizontal shift of the graph of $ y = x^2 $. If $ c $ is positive, the graph shifts to the left by $ c $ units. If $ c $ is negative, the graph shifts to the right by $ |c| $ units.

Step 3: Apply the Transformation

In the given function $ f(x) = (x + 15)^2 $, the term $ +15 $ indicates a horizontal shift to the left by 15 units.