Complete the square to find the y-value for the minimum value of the function-f(x)=x^2-8x+28

9514 1404 393

  12

Step-by-step explanation:

The square can be completed by adding and subtracting the square of half the linear term's coefficient.

  f(x) = x^2 -8x +(-8/2)^2 +28 -(-8/2)^2

  f(x) = (x^2 -8x +16) +(28 -16)

  f(x) = (x -4)^2 +12

The minimum value of the function is 12, when the squared term is zero.