Analysis: Showing a set can be bounded below in the reals

Question

How do I go about showing the set $A=\left\{x^2+6x+6 : x\in\mathbb{R}\right\}$ is bounded below in the reals. Further,how may I go about finding the greatest lower bound for $A$?

Thank you in advance

Hint. A describes a quadratic. What kind of shape is that? – John Douma Oct 10 '15 at 13:51 — John Douma, Oct 10 '15 at 13:51

score 3 · Answer 1 · answered Oct 10 '15 at 13:58

3

Hint. For this quadratic, completing the square will almost do it for you, i.e. writing $$x^2 + 6 x + 6=(x- a)^2 + b .$$ Then you can read off the infimum $b $.

answered Oct 10 '15 at 13:58

martini

84,101

Analysis: Showing a set can be bounded below in the reals

1 Answers1