## anonymous one year ago Identify the axis of symmetry and vertex of f(x) = –2x^2 –2x–1. Axis of symmetry: x = 0.5; Vertex: (0.5, – 0.50) Axis of symmetry: x = – 0.5; Vertex: (– 0.5, 0.50) Axis of symmetry: x = – 0.5; Vertex: (– 0.5, – 0.50) Axis of symmetry: x = 0.5; Vertex: (– 0.5, – 0.50)

1. anonymous

@fashionismybesty

2. anonymous

http://www.mathway.com/graph/NTUxODk this is an amazing site for graphing

3. freckles

Do you know how to write in vertex form? If involves completing the square? $f(x)=-2x^2-2x-1 \\ f(x)=-2(x^2+x)-1 \\ f(x)=-2(x^2+x+L)-1+2L \\ \text{ notice } -2L+2L=0 \\ \text{ we need to figure out what } L \text{ needs to be to } \\ \text{ complete the square inside that one ( )}$

4. Nnesha
5. triciaal

|dw:1440639916432:dw|

6. triciaal

vertex form a(x-h)^2 + k = 0 vertex (h, k) axis of symmetry x = h

7. anonymous

It's really confusing.

8. Nnesha

do you know what 's a b and c in the equation ?

9. anonymous

No.. I'm really confused with math, I sometimes know things but like need to refresh my mind.. I know some rules in Arabic and some in English.. Because I took math in both languages and now im really really confused

10. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @Nnesha or http://openstudy.com/study#/updates/55de281ae4b0f9297e9bc5e7 :=) $$\color{blue}{\text{End of Quote}}$$ didn't notice that link doesn't work http://openstudy.com/study#/updates/55daa403e4b0a0d51271c948

11. Nnesha

ahh i see okay

12. Nnesha

quadratic equation is $\huge\rm Ax^2+Bx+C=0$ where a=leading coefficient b=middle term c= constant term

13. Nnesha

quadratic equation is $\huge\rm\color{red}{ A}x^2+\color{blue}{B}x+\color{pink}{C}$ where a=leading coefficient b=middle term c= constant term $\huge\rm \color{Red}{–2}x^2 \color{blue}{–2}x\color{pink}{–1}$ so what is a and b equal to in that equation ?

14. Nnesha

let me if u didn't understand :=)

15. anonymous

2? @Nnesha

16. Nnesha

not just negative 2 a=-2 b=-2 now use the formula to find x-coordinate of vertex $\huge\rm \frac{ -b }{ 2a }$ replace b and a with -2

17. anonymous

so it would be -2/2^-2?

18. Nnesha

no $\frac{ -(-2) }{ 2(-2)}$ don't forget to put the parentheses there is negative sign in the formula and b is also negative and at the denominator it's 2 times -2 not 2 to the -2 power

19. Nnesha

2(-2) is n't same as 2^(-2)

20. anonymous

Ohh okay

21. Nnesha

now simplify that

22. anonymous

it would equal -2?

23. Nnesha

no

24. Nnesha

$\huge\rm \frac{ -(-2) }{ 2(-2)}$ what did you get at the numerator ?

25. anonymous

aren't we supposed to divide the numerator and denominator by -2

26. Nnesha

yes right $\huge\rm \frac{ -\cancel{(-2)} }{ 2\cancel{(-2)}}$ what would you get at the top ?

27. anonymous

the negative sign

28. anonymous

0?

29. Nnesha

no there is one

30. Nnesha

invisible one :=)

31. Nnesha

so it should be -1/2

32. Nnesha

just like 2/2 =1

33. anonymous

Oh okay

34. Nnesha

yes so that's the x-coordinate of the vertex which is also the axis of symmetry

35. Nnesha

now replace all x for -1/2 into the f(x) function

36. Nnesha

$\huge\rm f(-0.5) = –2x^2 –2x–1.$ -1/2 = -0.5 so now replace all x's for -0.5 then solve

37. anonymous

f(-0.5) = -2(-0.5)^2-2(0.5)-1

38. Nnesha

yes right now solve right side :=) to find y-coordinate of the vertex

39. anonymous

equals -0.5?

40. Nnesha

yes right that's y-coordinate of vertex

41. Nnesha

done!

42. anonymous

but the choices have 0.50.. from where did that come from @Nnesha

43. Nnesha

ohh that's the same .50 or .5

44. anonymous

so the answer is C) Axis of symmetry: x = – 0.5; Vertex: (– 0.5, – 0.50)

45. Nnesha

yep

46. Nnesha

subtract .50-.5 you will get 0 thats mean both are the same

47. anonymous

Oh thank you very much!

48. Nnesha

my pleasure!