anonymous one year ago Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = x + 8 Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). A)x = 3 B)x = 4 C)x = 5 D)x = 6

1. anonymous

@butterflydreamer @chrisdbest @brebre5564

2. anonymous

@CaptainLlama49

3. anonymous

@mathmate

4. anonymous

Lemme see

5. anonymous

OK

6. anonymous

its been a while since ive done this lol do you know what f(x) stands for cx

7. anonymous

NOP

8. anonymous

ARE YOU THERE?

9. anonymous

@CaptainLlama49

10. anonymous

11. anonymous

@Study_together

12. anonymous

@ospreytriple

13. anonymous

@Kash_TheSmartGuy

14. jtvatsim

Hmm... If I'm reading this right, it looks like they just want you to plug in different x values (from 1 to 6) into the equations.

15. jtvatsim

So, if we started with the "f(x)" equation we are thinking about \[-x^2 + 4x + 12\] and we want to plug in different x values to see what we get. What would you get if you plug in x =1?

16. anonymous

17. jtvatsim

Well, let's see. What did you do to get that answer?

18. anonymous

i calculate: −x2+4x+12

19. anonymous

\[f(x) = −x^2 + 4x + 12 \]\[g(x) = x + 8 \]\[f(x)=g(x)\iff -x^2+4x+12=x+8\]

20. jtvatsim

OK, that sounds right. Maybe there was just a calculation error. I did -(1)^2 + 4(1) + 12 = -1 + 4 + 12 = 15. Does that make sense?

21. anonymous

yes

22. jtvatsim

OK, so in the "f(x)" row under the "1" column you would fill in 15.

23. jtvatsim

You should have something like this so far 1 2 3 ..... f(x) 15 g(x)

24. jtvatsim

It's a little tedious, but we have to repeat our calculations for all x's up to 6. Next is x = 2. Plug that into -x^2 + 4x + 12 and see what you get. I'll check your answer. :)

25. anonymous

i get 6? i dont know if i'm right

26. jtvatsim

OK, can you write your steps like I did before?

27. anonymous

ok let me see

28. jtvatsim

29. anonymous

like this?

30. anonymous

f(x)=−x2+4x+12 g(x)=x+8 f(x)=g(x)⟺−x2+4x+12=x+8

31. jtvatsim

Well, not exactly. But good job copying all those formulas! :) I meant when you plug in x = 2 into -x2+4x+12. Like this -(2)^2 + 4(2) + 12 = ... What comes next?

32. jtvatsim

so, -(2)^2 = -4 and 4(2) = 8 so we get -(2)^2 + 4(2) + 12 = -4 + 8 + 12 = ... could you finish this part?

33. anonymous

16?

34. jtvatsim

Yes! Exactly! :D

35. jtvatsim

Good job! That's all I meant by "show your steps". Anyways, we now have the second piece of our table 1 2 3 f(x) 15 16 g(x) Does this make sense so far?

36. anonymous

yes

37. jtvatsim

OK, let's keep going. Next is x = 3. Let's plug this into -x^2 + 4x + 12 and see what we get. I'll help get you started: -(3)^2 + 4(3) + 12 = What comes next?

38. anonymous

=15?

39. jtvatsim

Good!

40. anonymous

so, whats nexts?

41. jtvatsim

Alright, so we still need to do the same thing for x = 4, x = 5, and x = 6. Then we will be done plugging into the -x^2 + 4x + 12 equation. See if you can do these: -(4)^2 + 4(4) + 12 = -(5)^2 + 4(5) + 12 = -(6)^2 + 4(6) + 12 =

42. anonymous

yea give a second

43. jtvatsim

Of course, that's a lot of numbers. :)

44. anonymous

.12 .7 .0

45. jtvatsim

Very good! You got them all!

46. jtvatsim

OK, phew... almost done. We have finally completed the first row of the table: 1 2 3 4 5 6 f(x) 15 16 15 12 7 0 g(x)

47. anonymous

so whats next's?

48. jtvatsim

Next is the easier formula. We do the same thing we did for f(x), but now for g(x). Plug in x = 1, x = 2, x = 3, x = 4, x = 5, and x = 6 into x + 8 (that's g(x)).

49. jtvatsim

As long as we don't get freaked out, we can see that this is pretty quick to figure out. 1 + 8 = 2 + 8 = 3 + 8 = 4 + 8 = 5 + 8 = 6 + 8 =

50. jtvatsim

These answers will go into the second row of our table.

51. anonymous

ok let me solve

52. anonymous

.9 .10 .11 .12 .13 .14

53. jtvatsim

Great job! You've got it!

54. jtvatsim

Let's put these into the table: 1 2 3 4 5 6 f(x) 15 16 15 12 7 0 g(x) 9 10 11 12 13 14

55. jtvatsim

Cool! The table is finished like the problem wanted. Their last question was, when does f(x) = g(x) ? We just have to look at the table and see when the two numbers are the same. Which x value seems to have the same number for both f(x) and g(x)?

56. anonymous

yea, f(x) and g(x) have the 12

57. jtvatsim

Good! There's the match, so x = ? to make this happen. Our choices are: A)x = 3 B)x = 4 C)x = 5 D)x = 6 What do you think?

58. anonymous

4?

59. jtvatsim

Yep! That's the one! If we weren't sure we could just confirm that -(4)^2 + 4(4) + 12 = 12 and 4 + 8 = 12 just like we wanted. Finally! We are done! Congrats!

60. anonymous

thank you so much! you explain good! can you help me with 3 more please?

61. jtvatsim

I wish I could, but I've got to go for now, I've got some of my own homework to finish. Sorry. :( Good luck! I'm sure someone else can help you out. :)

62. anonymous

its fine

63. jtvatsim

Have a good night, or morning, or whatever time it is where you are. :)

64. anonymous

night