Show that the function f(x) = x^2 + 2x + 2 is always positive for real values of x
By completing the square we find that f(x) = x2 + 2x + 2 = (x+1)2 + 1Since (x+1)2 is a number that has been squared, it must be greater than or equal to zero. Therefore, f(x) = (x+1)2 + 1 must be greater than zero because adding a positive number to a number that is greater than or equal to zero will always give a positive number.
