Question

what is the x-intercept of the graph of the function $f(x) = x^2 - 16x + 64$?
$\bigcirc$ $(-8, 0)$
$\bigcirc$ $(0, 8)$
$\bigcirc$ $(8, 0)$
$\bigcirc$ $(0, -8)$

Explanation:

Step1: Recall x-intercept definition

To find the x-intercept, set \( f(x) = 0 \), so solve \( x^2 - 16x + 64 = 0 \).

Step2: Factor the quadratic

The quadratic is a perfect square trinomial: \( x^2 - 16x + 64=(x - 8)^2 \).

Step3: Solve for x

Set \( (x - 8)^2 = 0 \), then \( x - 8 = 0 \), so \( x = 8 \).
The x-intercept is \( (8, 0) \) since the y - coordinate at x - intercept is 0.

Answer:

C. (8, 0) (assuming the options are labeled A to D with A: (-8, 0), B: (0, 8), C: (8, 0), D: (0, -8))