When (x – 2)^2 + 7 has a minimum value, what is the value of x?
First, expand (x-2)2:
= (x-2)(x-2),
= x2 - 2x - 2x + 4
= x2 - 4x + 4
Add on the +7:
= x2 - 4x + 11
complete the square
= (x - 2)2 - 4 + 11
= (x - 2)2 + 7
when the graph has a minumum value, (x - 2) = 0,
so x = 2
