What is the vertex of the quadratic function f(x)=(x-8)(x-2) ?

Multiply out f(x)=(x-8)(x-2):  f(x) = x^2 - 8x - 2x + 16, or f(x) = 1x^2 - 10x + 16.
Thus, a=1, b= -10 and c=16.

One of several ways to find the vertex involves "completing the square."

x^2 - 10x + 16 = x^2 - 10x + 25 - 25 + 16, or y = (x-5)^2 -9, or y+9=(x-5)^2.

Compare this result to y-k = a(x-h)^2.  We see that h=5 and k=-9.

Thus, the vertex is at (h,k) = (5, -9). 

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