To find the minimum value of x2−8x+20, complete the square.
Starting with:
x2−8x+20
Take the coefficient of x, which is −8, divide by 2 to get −4, then square to get 16.
Add and subtract 16:
x2−8x+20
=x2−8x+16−16+20
=(x−4)2−16+20
=(x−4)2+4
Since (x−4)2≥0 for all real x, the minimum value of (x−4)2 is 0.
This occurs when x=4.
The minimum value of the expression is:
(x−4)2+4
=0+4
=4
Therefore, the minimum value is 4.