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.