Quadratic Function y=(x-4)²: Analyzing a 4-Unit Horizontal Shift

$y=(x-4)^2$ is the displacement function $y=x^2$ right 4 steps

To solve this problem, we'll verify if $y = (x-4)^2$ is obtained by shifting $y = x^2$ four units to the right:

• Step 1: Identify transformation properties.
  The equation $y = (x-h)^2$ indicates a horizontal shift of the parent function $y = x^2$.
• Step 2: Determine the shift value from the expression.
  In $y = (x-4)^2$, $h = 4$. This implies a shift 4 units to the right because $h = 4$ is positive.
• Step 3: Verify the shift.
  If we replaced $x$ with $x-4$, this represents taking the graph of $y = x^2$ and shifting it rightwards by 4 units on the x-axis.

Therefore, we conclude that the function $y = (x-4)^2$ does represent a displacement of $y = x^2$ to the right by 4 units. Hence, the correct answer to the problem is True.