To find the x-intercept of the function, we need to determine where the graph crosses the x-axis. This occurs when the value of the function, f(x), is equal to zero.
Starting with the equation:
f(x) = x² – 16x + 64 = 0
This is a quadratic equation. We can solve it using factoring, the quadratic formula, or completing the square. In this case, we can factor the quadratic directly:
f(x) = (x – 8)(x – 8) = 0
Setting each factor equal to zero gives us:
x – 8 = 0
x = 8
Thus, the x-intercept is at the point (8, 0). This means the graph of the function touches the x-axis at x = 8.
In summary, the x-intercept of the graph of the function f(x) = x² – 16x + 64 is located at the point (8, 0).