SOLUTION: Show that {{{f(x)=x^2+6x+12}}} is always positive for all values of x

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Question 1135104: Show that f%28x%29=x%5E2%2B6x%2B12 is always positive for all values of x
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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x%5E2+%2B+6x+%2B+12 = %28x%5E2+%2B+6x+%2B+9%29 + 3 = %28x%2B3%29%5E2 + 3.


So, this expression is the sum of two terms.


First term is quadratic binomial  %28x%2B3%29%5E2,  which ALWAYS is non-negative as a square of a real number.


The second term is constant term "3", which is positive, too.


Therefore, their sum is ALWAYS positive.


Thus, the original expression is always positive, too.

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It is a TEMPLATE and a SAMPLE to you on how this and similar problems should be solved and worded.

The method which I used  is called "completing the square".

On how this method works,  you can read from the lesson
    - HOW TO complete the square - Learning by examples
in this site.


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