Find C so that the vertex of the parabola y=x^2-8x+c is a point on the x axis
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