## anonymous one year ago please help me The graphs of f(x) and g(x) are shown below: graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 9, 0. If f(x) = (x + 7)2, which of the following is g(x) based on the translation?

1. anonymous
2. Michele_Laino

I'm sorry, I'm not able to see your graphs

3. anonymous

@Michele_Laino sorry i had an emergency hold on

4. anonymous

@Michele_Laino

5. Michele_Laino

hint: the graph of f(x), can be obtained from the graph of g(x), making a traslation by 2 units to right

6. Michele_Laino

or, vice versa, the graph of g(x), can be obtained from the graph of f(x), making a traslation by2 units to left

7. Michele_Laino

the last condition, can be expressed by this formula: $\Large g\left( x \right) = f\left( {x + 2} \right)$

8. anonymous

im still sort of confused

9. anonymous

If f(x) = (x + 7)2, which of the following is g(x) based on the translation? g(x) = (x + 9)2 g(x) = (x + 5)2 g(x) = (x − 9)2 g(x) = (x − 5)2 theres are the choice they gave me

10. Michele_Laino

in other words, you have to replace x, with x+2 into the expression of f(x), namely: $\Large g\left( x \right) = f\left( {x + 2} \right) = {\left( {x + 2 + 7} \right)^2} = ...$

11. anonymous

o ok it said +5 so i was totally confused

12. anonymous

ok so i understand it would be A then?

13. Michele_Laino

no, sorry I have made a typo

14. anonymous

so it isnt A?

15. Michele_Laino

yes! correct! it is option A

16. anonymous

ok thank you so much can you help with a few more?

17. Michele_Laino

ok!

18. anonymous

19. anonymous

ok im ready Which graph shows the quadratic function y = 3x2 + 12x + 14?

20. anonymous

@Michele_Laino

21. Michele_Laino

your function is a parabola, right?

22. anonymous

yes it is

23. Michele_Laino

the equation of the axis of your parabola, is: $\Large x = - \frac{{12}}{{2 \cdot 3}} = ...$

24. Michele_Laino

which is the x-coordinate of the vertex. please complete: $\Large x = - \frac{{12}}{{2 \cdot 3}} = ...?$

25. anonymous

-2?

26. Michele_Laino

correct! the equation of the axis of your parabola, is x=-2, furthermore, the x-coordinate of the vertex of your parabola, is also x=-2

27. anonymous

so the answer would be graph a because its the only one with negative 2 aas the x coordinate

28. anonymous

o nvm it could also be c

29. anonymous

but i think it is a

30. Michele_Laino

ok! we have to understand what is the right graph: A or C?

31. anonymous

i think a because its at -2,-2

32. Michele_Laino

the y-coordinate of your parabola is: $\Large y = \frac{{4ac - {b^2}}}{{4a}}$ where a=3, b=12, and c=14

33. Michele_Laino

oops..it is the y-coordinate of the vertex of your parabola

34. anonymous

so it is not a?

35. Michele_Laino

so after a substitution, we get: $\Large y = \frac{{4ac - {b^2}}}{{4a}} = \frac{{4 \cdot 3 \cdot 14 - {{12}^2}}}{{4 \cdot 3}} = ...?$ please complete

36. anonymous

1sec let me do it

37. Michele_Laino

ok!

38. anonymous

-2 again so it is a

39. Michele_Laino

are you sure? I got a different result

40. Michele_Laino

$\large y = \frac{{4ac - {b^2}}}{{4a}} = \frac{{4 \cdot 3 \cdot 14 - {{12}^2}}}{{4 \cdot 3}} = \frac{{168 - 144}}{{12}} = ...?$

41. anonymous

yes that what i got 168 - 144 i did it wrong its positive 2 but i used thos step

42. anonymous

so its c for some reason i added a negtive signat the end of the problem

43. Michele_Laino

correct! it is option C

44. anonymous

thank you so much

45. Michele_Laino

:)

46. anonymous

can u help with 1 more

47. anonymous

Which of the following represents the factored form of f(x) = x3 − 64x?

48. anonymous

@Michele_Laino

49. Michele_Laino

ok! I'm here

50. anonymous

k can you help me with this 1 Which of the following represents the factored form of f(x) = x3 − 64x?

51. Michele_Laino

yes!

52. Michele_Laino

first step: we can factor out x, so we can write this: $\Large {x^3} - 64x = x\left( {{x^2} - 64} \right)$

53. Michele_Laino

subsequently, we can use this algebraic identity: $\Large {A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right)$ where A=x, and B= 8

54. anonymous

we have to foil this right if so can you show me how i would set it up?

55. Michele_Laino

no, it is not necessary to apply the foil method, since we have to apply that standard identity

56. Michele_Laino

you should get this: $\Large {x^2} - 64 = \left( {x - 8} \right)\left( {x + 8} \right)$

57. anonymous

theses are the choices f(x) = x(x + 8)(x − 8) f(x) = (x − 8)(x + 8) f(x) = x(x − 8)2 f(x) = x(x2 − 8)

58. Michele_Laino

so, the complete factorization, is: $\Large {x^3} - 64x = x\left( {{x^2} - 64} \right) = x\left( {x - 8} \right)\left( {x + 8} \right)$

59. anonymous

o ok so i just needed to find wat squared equals 64 ok so its b

60. Michele_Laino

I think it is option A

61. anonymous

o ok you are right i see my error with the x variable

62. anonymous

ay thank you so much michele u were really helpfull :) lol and u have a sexy as name

63. Michele_Laino

thanks! :)