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anonymous

  • one year ago

Rewrite the equation y = 3x^2 + 6x + 2 in the alternate form and state the vertex point.

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  1. jim_thompson5910
    • one year ago
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    do you see how y = 3x^2 + 6x + 2 is in the form y = ax^2 + bx + c ?

  2. anonymous
    • one year ago
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    a = 3 b = 6 c = 2?

  3. jim_thompson5910
    • one year ago
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    yep

  4. jim_thompson5910
    • one year ago
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    now plug the values of a,b into h = -b/(2a) what is the value of h?

  5. anonymous
    • one year ago
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    h = -1?

  6. jim_thompson5910
    • one year ago
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    yes

  7. jim_thompson5910
    • one year ago
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    now plug that value in for x to find y y = 3x^2 + 6x + 2 y = 3(-1)^2 + 6(-1) + 2 y = ???

  8. anonymous
    • one year ago
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    Is it -1?

  9. jim_thompson5910
    • one year ago
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    correct

  10. jim_thompson5910
    • one year ago
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    so k = -1

  11. jim_thompson5910
    • one year ago
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    we have a = 3, h = -1 and k = -1 plug those into y = a(x-h)^2 + k

  12. anonymous
    • one year ago
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    Does x = 6?

  13. jim_thompson5910
    • one year ago
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    where are you getting x = 6 ?

  14. anonymous
    • one year ago
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    Oh thought x = 6 from the problem. Dont know what x is.

  15. jim_thompson5910
    • one year ago
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    x is just a variable to be left alone really

  16. jim_thompson5910
    • one year ago
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    what did you get when you plugged those values into y = a(x-h)^2 + k

  17. anonymous
    • one year ago
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    Is it 11?

  18. jim_thompson5910
    • one year ago
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    don't replace x though

  19. anonymous
    • one year ago
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    Oh keep x as just x?

  20. jim_thompson5910
    • one year ago
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    yes

  21. anonymous
    • one year ago
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    So is this right? y - 3(x - (-1)^2 + - 1 . I think I set it up wrong.

  22. anonymous
    • one year ago
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    I meant y =

  23. jim_thompson5910
    • one year ago
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    if you simplified that, you'd get what?

  24. anonymous
    • one year ago
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    Does the 3 go with the things inside the ( )

  25. jim_thompson5910
    • one year ago
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    no

  26. jim_thompson5910
    • one year ago
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    |dw:1442024648925:dw|

  27. jim_thompson5910
    • one year ago
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    |dw:1442024665299:dw|

  28. jim_thompson5910
    • one year ago
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    |dw:1442024695181:dw|

  29. jim_thompson5910
    • one year ago
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    I think you were asking if 3 goes inside the parenthesis? or were you asking if the 3 was being multiplied with the (x-h)^2 term?

  30. anonymous
    • one year ago
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    Yeah does the 3 multiply with that?

  31. jim_thompson5910
    • one year ago
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    yes the 3 and \(\Large (x-(-1))^2\) are being multiplied it's like saying `3x` is the same as `3 times x`

  32. jim_thompson5910
    • one year ago
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    what does `x-(-1)` simplify to?

  33. anonymous
    • one year ago
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    3x - (-3)^2 - (-1) ?

  34. jim_thompson5910
    • one year ago
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    if you subtract a negative, what are you really doing?

  35. anonymous
    • one year ago
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    Making it positive?

  36. jim_thompson5910
    • one year ago
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    yeah adding so `x-(-1)` is the same as `x+1`

  37. jim_thompson5910
    • one year ago
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    making \[\Large y=3(x-(-1))^2+(-1)\] turn into \[\Large y=3(x+1)^2-1\]

  38. anonymous
    • one year ago
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    Oh okay I see.

  39. jim_thompson5910
    • one year ago
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    What would be the vertex here?

  40. anonymous
    • one year ago
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    I am not really sure.

  41. anonymous
    • one year ago
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    Do you put everything together?

  42. jim_thompson5910
    • one year ago
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    well the general vertex form equation \[\Large y = a(x-h)^2 + k\] has the vertex `(h,k)`

  43. anonymous
    • one year ago
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    (1, -1) ?

  44. jim_thompson5910
    • one year ago
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    well recall that h = -1 and k = -1

  45. anonymous
    • one year ago
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    Oh thats not the vertex?

  46. jim_thompson5910
    • one year ago
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    no but you're close

  47. anonymous
    • one year ago
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    I do not get how to find it.

  48. jim_thompson5910
    • one year ago
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    it's (-1,-1) you start with (h,k) and replace h and k with the values we got earlier

  49. jim_thompson5910
    • one year ago
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    h = -b/(2a) = -1 after plugging in a and b k = -1 after plugging x = -1 into the original equation

  50. anonymous
    • one year ago
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    Oh I see where it came from.

  51. anonymous
    • one year ago
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    Is the vertex (-1, -1) or is that used to find the vertex?

  52. jim_thompson5910
    • one year ago
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    that is the vertex as you can see on this graph, it's the lowest point or the min point https://www.desmos.com/calculator/idhk1vx8ar

  53. anonymous
    • one year ago
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    Oh okay and then y = 3(x + 1)^2 - 1 is the equation rewritten?

  54. anonymous
    • one year ago
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    in the alternate form*

  55. jim_thompson5910
    • one year ago
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    that's vertex form, yes

  56. anonymous
    • one year ago
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    Oh okay thanks for your help. I am very slow in math as anyone can tell.

  57. jim_thompson5910
    • one year ago
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    you're doing fine

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