## burhan101 3 years ago Increasing and decreasing intervals of 4x^2+4x-1

1. etemplin

do you know derivatives?

2. burhan101

we have to complete the square

3. burhan101

would it be \[\huge 4x^2+4x-4+4-1 \] for the first step of completing the square ?

4. etemplin

yes

5. burhan101

then \[\huge 4 (x-1)^2 -1\] ? :S

6. etemplin

when you multiply that out it doesnt give you 4x^2+4x-4+4-1

7. etemplin

try this one 4(x+(1/2))^2 -2

8. burhan101

i dont get where the 1/2 comes from :S

9. etemplin

i found the error: the leading coefficient must be 1 to complete the square try setting it equal to 0, moving the -1 over, and dividing by 4 then complete the square

10. burhan101

why does it have to be 1 ?

11. etemplin

because thats what the formula says

12. burhan101

oh so it applies at all equations ?

13. etemplin

14. burhan101

|dw:1351571054966:dw|

15. etemplin

that works move the -1/4 over divide the middle term by 2 and square it add that answer to both sides factor

16. etemplin

*by middle term, i meant the coefficient with the x^1

17. burhan101

what do you mean by move the -1/4 over ? like why

18. etemplin

because thats what the formula says to do you'll end up with x^2+x=(1/4) the term with x is 1 (1/2)^2 = 1/4 add (1/4) to both sides end up with x^2+x+(1/4) = (1/2) factor into (x+(1/2))^2 = (1/2) solve for x

19. burhan101

|dw:1351571511476:dw|

20. etemplin

yes now factor the left side