Analyzing (x+4)² vs x²: Understanding Horizontal Shifts in Quadratic Functions

To solve this problem, we'll determine how the transformation $y = (x+4)^2$ affects the graph of $y = x^2$.

The function $y = x^2$ is a standard parabola centered at the origin.

In $y = (x+4)^2$, the positive number inside the parentheses indicates a transformation that moves the entire graph horizontally.

• Specifically, the expression $(x + 4)$ means we take the original $x$ value and add 4 to it before squaring, effectively shifting the graph.

According to properties of horizontal translations, when you add a positive number to $x$ inside the function—here, the +4 in $(x+4)$—the graph of the function $y = x^2$ shifts 4 units to the left along the x-axis.

Therefore, the transformation described by $y = (x+4)^2$ is indeed the graph of $y = x^2$ moved 4 spaces to the left.

Thus, the correct answer to this problem is Yes.