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