To find the [tex]\( x \)[/tex]-intercepts of the function [tex]\( f(x) = x^2 - 16x + 64 \)[/tex], we need to solve for [tex]\( x \)[/tex] when [tex]\( f(x) = 0 \)[/tex].
1. Start with the function:
[tex]\[
f(x) = x^2 - 16x + 64
\][/tex]
2. Set [tex]\( f(x) \)[/tex] equal to 0:
[tex]\[
x^2 - 16x + 64 = 0
\][/tex]
3. Solve the quadratic equation:
Notice that we can factor the quadratic equation [tex]\( x^2 - 16x + 64 \)[/tex]:
[tex]\[
x^2 - 16x + 64 = (x - 8)^2 = 0
\][/tex]
4. Set the factored form equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[
(x - 8)^2 = 0
\][/tex]
5. Take the square root of both sides:
[tex]\[
x - 8 = 0
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 8
\][/tex]
Therefore, the [tex]\( x \)[/tex]-intercept is at [tex]\( x = 8 \)[/tex]. The coordinate of the [tex]\( x \)[/tex]-intercept is:
[tex]\[
(8, 0)
\][/tex]
Thus, the correct answer is [tex]\( (8, 0) \)[/tex].
