Find Y-Axis Intersection of y=(x-6)²: Quadratic Function Analysis

To find the intersection of the function $y = (x-6)^2$ with the y-axis, we follow these steps:

• Step 1: Identify the known function and approach the problem by setting $x = 0$ since we are looking for the intersection with the y-axis.

• Step 2: Substitute $x = 0$ into the equation $y = (x-6)^2$.

• Step 3: Perform the calculation to find $y$.

Now, execute these steps:
Step 1: We are given the function $y = (x-6)^2$.
Step 2: Substitute $x = 0$ into the equation:
$y = (0-6)^2$
Step 3: Simplify the expression:
$y = (-6)^2 = 36$

The point of intersection with the y-axis is therefore $(0, 36)$.

Thus, the solution to the problem is $(0, 36)$.