To find the x-intercept of the function f(x) = x² – 16x + 64, we need to determine the points where the graph intersects the x-axis. This occurs when the value of f(x) equals 0. Therefore, we set the equation equal to zero:
x² – 16x + 64 = 0
This is a quadratic equation, and we can solve it using different methods: factoring, completing the square, or the quadratic formula. In this case, let’s start by factoring:
We look for two numbers that multiply to 64 (the constant term) and add up to -16 (the coefficient of the linear term). The numbers that fit are both -8:
(x – 8)(x – 8) = 0 or (x – 8)² = 0
Now, we solve for x:
x – 8 = 0
From this, we find:
x = 8
Thus, the x-intercept of the graph of the function is at the point (8, 0). This means that when we plot the function, it will cross the x-axis at x = 8.
In summary, when asked about the x-intercept of the function f(x) = x² – 16x + 64, we find that it is located at the point (8, 0).