Question

In the function f(x)=(x-2)^2+4, the minimum value occurs when x is

Answer 1

The graph of the function is a parabola. 

The nose comes down as far as y=4 but no farther.

That happens when  (x - 2)² = 0 , and THAT happens when x = 2 .

Answer 2

F(x) = (x - 2)² + 4
f(x) = (x - 2)(x - 2) + 4
f(x) = (x(x - 2) - 2(x - 2)) + 4
f(x) = (x(x) - x(2) - 2(x) + 2(2)) + 4
f(x) = (x² - 2x - 2x + 4) + 4
f(x) = (x² - 4x + 4) + 4
f(x) = x² - 4x + 4 + 4
f(x) = x² - 4x + 8

$x = -\frac{b}{2a} = -\frac{-4}{2(1)} = -\frac{-4}{2} = -(-2) = 2$