## iwanttogotostanford one year ago Please HELP: Using the completing-the-square method, rewrite f(x) = x^2 + 4x − 1 in vertex form. f(x) = (x + 2)^2 + 1 f(x) = (x + 2)^2 f(x) = (x + 2)^2 + 4 f(x) = (x + 2)^2 − 5

1. jdoe0001

do you know what a "perfect square trinomial" is? sometimes just called a "perfect square"

2. iwanttogotostanford

yes

3. zzr0ck3r

$x^2+bx+c=(x+\frac{b}{2})^2+c-\frac{b^2}{4}$

4. iwanttogotostanford

would it be D then?

5. Jhannybean

$f(x) = x^2+4x-1$$=(x^2+4x)-1$$=(x^2+4x+\color{red}{4})-1\color{red}{-4}$$=\boxed{(x-2)^2-5}$

6. jdoe0001

so... $$\bf f(x)=x^2+4x-1\implies f(x)=(x^2+4x+{\color{red}{ \square ?}}^2)-1$$ what do you think is the missing number?

7. Jhannybean

Lovely.

8. zzr0ck3r

correct @iwanttogotostanford

9. iwanttogotostanford

one more?

10. Jhannybean

@jdoe0001 why isn't \boxed working for me?

11. iwanttogotostanford

Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 6x + ___? 1 3 6 9

12. iwanttogotostanford

i believe its 9 but i just want to make sure

13. Jhannybean

$c=\left(\frac{6}{2}\right)^2 = ~?$

14. iwanttogotostanford

9!

15. Jhannybean

$\color{red}{\checkmark}$

16. iwanttogotostanford

i really need help with this one real quick, thanks for all your help..:-)

17. iwanttogotostanford

Solve x2 + 8x − 3 = 0 using the completing-the-square method. x = four plus or minus the square root of three x = negative four plus or minus the square root of three x = four plus or minus the square root of nineteen x = negative four plus or minus the square root of nineteen

18. Jhannybean

use the method we used above.

19. iwanttogotostanford

so , B?

20. Jhannybean

I don't know,I didn't solve it.

21. iwanttogotostanford

could you help me? :_)

22. Jhannybean

first add +3 to both sides.

23. Jhannybean

what do you get, @iwanttogotostanford ?

24. iwanttogotostanford

the same but on the left -6 and on the right 3

25. Jhannybean

??....

26. Jhannybean

okay, if you add +3 to both sides , the answer i was looking for is, x$$^2$$+8x=3

27. iwanttogotostanford

@Jhannybean sorry, i was gone