What is the x-intercept of the graph of the function f (x) = x2 - 16x + 64?

Immediately, we can try to split the middle term.

x^2 - 16x + 64

The factor of 64 that satisfies the criteria is - 8 * - 8.

Because our leading coefficient is 1, we immediately know the simplified form of this polynomial is (x - 8) (x - 8)

Even though this is a second degree polynomial, we only have one x-intercept, because it is multiplicity two.

When you have a factor with multiplicity two, or any even number, the line will dip through that x value, and then go back up, like a parabola.

The x-intercept of the graph is 8, with multiplicity two.