# Thread: Completing the square [finding a maximum and minimum value]?

1. ## Completing the square [finding a maximum and minimum value]?

If I had the quadratic expression of x^2 + 6x - 4, and wrote it as (x + 3)^2 + 5, what would be the minimum and maximum values of this and why?

2. Originally Posted by db5vry
If I had the quadratic expression of x^2 + 6x - 4, and wrote it as (x + 3)^2 + 5, what would be the minimum and maximum values of this and why?
The minimum value would be 5. This would occur at x = -3 because a squared value cannot be negative so it will be a minimum when (x+3) = 0.

The maximum would be infinity

3. When completing the square of $x^2+6x-4$ I get $(x+3)^2-13$ since $(x+3)^2=x^2+6x+9$, so to get from 9 to -4 you need to minus 13.

4. Originally Posted by db5vry
If I had the quadratic expression of x^2 + 6x - 4, and wrote it as (x + 3)^2 + 5
In this case, as Chella pointed out, you have the wrong expression. 9+ 5 is NOT equal to -4.

what would be the minimum and maximum values of this and why?