what value of x can minimize the value of: (3-x)2 + (8-x)2 + (13-x)2 ?

Question

don't know how to solve this question for a stats class?  We folied and got:  242-48x+3x2?

Answer 1

I will continue from 3x^2 - 48x + 242, which is what you got.

3x^2 - 48x + 242
= (3x^2 - 48x) + 242
= 3(x^2 - 16x) + 242
= 3(x - 8)^2 - 3(64) + 242
= 3(x - 8)^2 - 192 + 242
= 3(x - 8)^2 + 50

Notice that 3(x - 8)^2 >= 0 for all real values of x.
Hence, the value of x which will result in the minimum value of 3(x - 8)^2 + 50 will be x = 8.