Finding X-Intercepts of y=(x-1/2)²: Quadratic Function Analysis

To find the intersection of the parabola $y = (x - \frac{1}{2})^2$ with the x-axis, we need to set $y = 0$ because at the x-axis, the y-coordinate is always zero.

Let's go through the steps:

• Step 1: Set the equation equal to zero: $(x - \frac{1}{2})^2 = 0$.
• Step 2: Solve for $x$. A square equals zero only when the base itself is zero, thus:
  $x - \frac{1}{2} = 0$
• Step 3: Solve this equation for $x$:
  $x = \frac{1}{2}$

The intersection point on the x-axis has coordinates $(x, y)$, where we have found $x = \frac{1}{2}$ and we know $y = 0$.

Therefore, the intersection of the function with the x-axis is at the point $(\frac{1}{2}, 0)$.

Thus, the correct answer is choice 3: $(\frac{1}{2}, 0)$.