x value of vertex = -b/2a where b = -8 and a = 1

8/2 = 4

If the vertex lies on the x-axis, the y value must be zero, so we plug in the point (4, 0) to find C:

0 = (4)^2 - 8(4) + C

0 = 16 - 32 + C

0 = -16 + C

16 = C

There you go.

y = x^2 - 8x + 16

To verify it even further we solve for x:

0 = (x-4)(x-4)

Thus x = 4