## anonymous one year ago Using the completing-the-square method, rewrite f(x) = x2 + 4x − 1 in vertex form

1. anonymous

Group the terms like this $f(x)=(x^2+4x)-1$ Take the coefficient of x, divide it by 2 and square it. What's $$\left( \frac{ 4 }{ 2 } \right)^2$$ ?

2. anonymous

4

3. anonymous

Right, so add 4 inside the parentheses. This means you also have to subtract 4 outside, so the equation doesn't change. $f(x)=(x^2+4x+4)-1-4$

4. anonymous

Now factor the part in parentheses, and combine like terms on the outside

5. anonymous

so would it be f(x)=(x^2+4x+4)-5

6. anonymous

yes, but you also have to factor x² + 4x + 4

7. anonymous

oh I got it. But can you help me with a few others?

8. anonymous

ok

9. anonymous

Using the completing-the-square method, find the vertex of the function f(x) = –2x2 + 12x + 5 and indicate whether it is a minimum or a maximum and at what point.

10. anonymous

$$f(x)=-2x^2+12x+5$$ Group it again $$f(x)=(-2x^2+12x)+5$$ This time, because you have -2 in front of x², you have to factor it out. Can you do that?

11. anonymous

would it be f(x)=-2(x^2+12x)+5

12. anonymous

no, you have to divide 12 by -2 as well because it's also in parentheses

13. anonymous

so it would be 6?

14. anonymous

12/(-2)= -6 So you have $f(x)=-2(x^2-6x)+5$ Now take the coefficient of x, that's -6. Divide it by 2, the square the result like we did above

15. anonymous

okay so would it be minimum or maximum?

16. anonymous

the number in front of x² is negative, so it's a maximum

17. anonymous

okay so whats the point? (-3,5)?

18. anonymous

You have to complete the square to find the point

19. anonymous

If you don't want to do it that way, use $x=-\frac{ b }{ 2a }$

20. anonymous

okay I just reset my exam so now I have different questions

21. anonymous

ughhhh I need help