Determine Point A on the Quadratic Function: f(x) = x² - 8x + 16

Let's solve the problem by following the outlined analysis:

• Step 1: Identify important points on the parabola.
• Step 2: Calculate the y-intercept by evaluating $f(0)$.
• Step 3: Confirm understanding of the vertex form and its characteristics.

Step 1: Identify the significant points on the function.
The function given is $f(x) = x^2 - 8x + 16$.

This function can be seen as
$f(x) = (x - 4)^2$.

This format not only indicates it is always non-negative but also reveals the vertex is located at $x = 4$, importantly, with $f(x) = 0$.

Step 2: Calculate the y-intercept.
Evaluate the function at $x = 0$:

$f(0) = 0^2 - 8 \cdot 0 + 16 = 16$.
So, the y-intercept is $(0, 16)$.

Thus, point A, which is often labeled at a crucial intercept, corresponds to the y-intercept of the function. The calculation confirms that point A is $(0, 16)$.

Therefore, the solution to the problem is $(0,16)$.