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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

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  1. anonymous
    • one year ago
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    @butterflydreamer @chrisdbest @brebre5564

  2. anonymous
    • one year ago
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    @CaptainLlama49

  3. anonymous
    • one year ago
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    @mathmate

  4. anonymous
    • one year ago
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    Lemme see

  5. anonymous
    • one year ago
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    OK

  6. anonymous
    • one year ago
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    its been a while since ive done this lol do you know what f(x) stands for cx

  7. anonymous
    • one year ago
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    NOP

  8. anonymous
    • one year ago
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    ARE YOU THERE?

  9. anonymous
    • one year ago
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    @CaptainLlama49

  10. anonymous
    • one year ago
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    Sorry lol cant help you there

  11. anonymous
    • one year ago
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    @Study_together

  12. anonymous
    • one year ago
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    @ospreytriple

  13. anonymous
    • one year ago
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    @Kash_TheSmartGuy

  14. jtvatsim
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    the answer its 6?

  17. jtvatsim
    • one year ago
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    Well, let's see. What did you do to get that answer?

  18. anonymous
    • one year ago
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    i calculate: −x2+4x+12

  19. anonymous
    • one year ago
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    \[f(x) = −x^2 + 4x + 12 \]\[g(x) = x + 8 \]\[f(x)=g(x)\iff -x^2+4x+12=x+8\]

  20. jtvatsim
    • one year ago
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    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
    • one year ago
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    yes

  22. jtvatsim
    • one year ago
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    OK, so in the "f(x)" row under the "1" column you would fill in 15.

  23. jtvatsim
    • one year ago
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    You should have something like this so far 1 2 3 ..... f(x) 15 g(x)

  24. jtvatsim
    • one year ago
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    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
    • one year ago
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    i get 6? i dont know if i'm right

  26. jtvatsim
    • one year ago
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    OK, can you write your steps like I did before?

  27. anonymous
    • one year ago
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    ok let me see

  28. jtvatsim
    • one year ago
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    sure, take your time. :)

  29. anonymous
    • one year ago
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    like this?

  30. anonymous
    • one year ago
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    f(x)=−x2+4x+12 g(x)=x+8 f(x)=g(x)⟺−x2+4x+12=x+8

  31. jtvatsim
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    16?

  34. jtvatsim
    • one year ago
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    Yes! Exactly! :D

  35. jtvatsim
    • one year ago
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    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
    • one year ago
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    yes

  37. jtvatsim
    • one year ago
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    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
    • one year ago
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    =15?

  39. jtvatsim
    • one year ago
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    Good!

  40. anonymous
    • one year ago
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    so, whats nexts?

  41. jtvatsim
    • one year ago
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    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
    • one year ago
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    yea give a second

  43. jtvatsim
    • one year ago
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    Of course, that's a lot of numbers. :)

  44. anonymous
    • one year ago
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    .12 .7 .0

  45. jtvatsim
    • one year ago
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    Very good! You got them all!

  46. jtvatsim
    • one year ago
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    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
    • one year ago
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    so whats next's?

  48. jtvatsim
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    These answers will go into the second row of our table.

  51. anonymous
    • one year ago
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    ok let me solve

  52. anonymous
    • one year ago
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    .9 .10 .11 .12 .13 .14

  53. jtvatsim
    • one year ago
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    Great job! You've got it!

  54. jtvatsim
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    yea, f(x) and g(x) have the 12

  57. jtvatsim
    • one year ago
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    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
    • one year ago
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    4?

  59. jtvatsim
    • one year ago
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    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
    • one year ago
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    thank you so much! you explain good! can you help me with 3 more please?

  61. jtvatsim
    • one year ago
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    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
    • one year ago
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    its fine

  63. jtvatsim
    • one year ago
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    Have a good night, or morning, or whatever time it is where you are. :)

  64. anonymous
    • one year ago
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    night

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