To find the \( x \)-intercept of the function \( f(x) = x^2 - 16x + 64 \), we need to set the function equal to zero and solve for \( x \).
[tex]\[ f(x) = x^2 - 16x + 64 \][/tex]
Step-by-step solution:
1. Set the function equal to zero:
[tex]\[
x^2 - 16x + 64 = 0
\][/tex]
2. Factor the quadratic expression:
The quadratic expression can be factored as:
[tex]\[
(x - 8)^2 = 0
\][/tex]
3. Solve for \( x \):
Since \((x - 8)^2 = 0\), we have:
[tex]\[
x - 8 = 0 \implies x = 8
\][/tex]
The \( x \)-intercept is the point where the graph crosses the \( x \)-axis. For this quadratic function, the \( x \)-intercept will be at \( x = 8 \).
Hence, the \( x \)-intercept is:
[tex]\[ (8, 0) \][/tex]
Therefore, the correct answer is:
[tex]\[ (8, 0) \][/tex]
