Solve (x-5)² = 0: Finding X-Axis Intersections of a Quadratic Function

To find the intersection of the parabola $y = (x-5)^2$ with the x-axis, we must set the value of $y$ to zero since any point on the x-axis has a y-coordinate of zero.

Solving the equation:

• Set $(x-5)^2 = 0$.
• To solve for $x$, remove the square by taking the square root of both sides. This yields $x-5 = 0$.
• Solve for $x$ by adding 5 to both sides: $x = 5$.

Thus, the intersection point of the parabola with the x-axis is at $(5, 0)$.

Therefore, the correct answer is $\boxed{(5,0)}$, which corresponds to choice 3.