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Breno

  • 2 years ago

The curve above is the graph of a degree 3 polynomial. It goes through the point (5,−6.3). what is the polynomial please? image attached

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  1. Breno
    • 2 years ago
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  2. SerikMB
    • 2 years ago
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    a sum of several terms produces a polynomial

  3. Breno
    • 2 years ago
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    i dont get what you mean

  4. SerikMB
    • 2 years ago
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    look at this http://www.mathsisfun.com/algebra/polynomials.html

  5. SerikMB
    • 2 years ago
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    here it is ax^3+bx^2+cx+d

  6. Breno
    • 2 years ago
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    so is 5 a and -6.3 b?

  7. SerikMB
    • 2 years ago
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    nope

  8. Breno
    • 2 years ago
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    how do i determine a an

  9. Breno
    • 2 years ago
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    and b

  10. SerikMB
    • 2 years ago
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    x=5 and y=-6.3

  11. SerikMB
    • 2 years ago
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    using the graph u should find a, b, c and d

  12. Breno
    • 2 years ago
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    how so?

  13. SerikMB
    • 2 years ago
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    is it the right graph?

  14. Breno
    • 2 years ago
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    yes

  15. SerikMB
    • 2 years ago
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    x intercepts here are 2 and -2

  16. cwrw238
    • 2 years ago
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    as you can see from the graph another 2 points through which it passes are (0,-2) and (0,2)

  17. satellite73
    • 2 years ago
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    this one has a zero at \(-2\) and a zero at \(2\) with multiplicity 2

  18. cwrw238
    • 2 years ago
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    sorry i mean (2,0) and (-2,0)

  19. satellite73
    • 2 years ago
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    making it \[a(x+2)(a-2)^2\] and your last job is to find \(a\)

  20. satellite73
    • 2 years ago
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    since you know it goes through \((5,-6.3)\) replace \(x\) by \(5\), set the result equal to \(-6.3\) and solve for \(a\)

  21. Breno
    • 2 years ago
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    so -6.3=(5+2)(a-2)^2?

  22. satellite73
    • 2 years ago
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    i am not sure, however, how you know it goes through that point, because it doesn't really look like it

  23. satellite73
    • 2 years ago
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    no, you need to solve for \(a\)

  24. satellite73
    • 2 years ago
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    replace \(x\) by \(5\) not by \(a\)

  25. satellite73
    • 2 years ago
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    \[ -6.3=a(5+2)(5-2)^2\]

  26. satellite73
    • 2 years ago
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    \[-6.3=7\times 9 a\] etc

  27. Breno
    • 2 years ago
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    so a=-0.1

  28. Breno
    • 2 years ago
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    ??

  29. cwrw238
    • 2 years ago
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    -6.3 / 63 = - 0.1 yes

  30. Breno
    • 2 years ago
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    so ax^3+bx^2+cx+d how do i fit all this into this format

  31. cwrw238
    • 2 years ago
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    expand -0.1(x +2)(x - 2)^2

  32. Breno
    • 2 years ago
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    -0.1x^3 + 0.2x^2 + 0.4x - 0.8???

  33. cwrw238
    • 2 years ago
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    yes

  34. Breno
    • 2 years ago
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    one last one

  35. Breno
    • 2 years ago
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    The curve above is the graph of a degree 4 polynomial. It goes through the point (5,−202.5). Find the polynomial

  36. Breno
    • 2 years ago
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  37. cwrw238
    • 2 years ago
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    satellite confused me at first when in his 2nd post he typed a instead of x. he made a human error which we all can make sometimes.

  38. Breno
    • 2 years ago
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    oh ok

  39. cwrw238
    • 2 years ago
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    this can be dome in similar way to the first curve there are zeros at =4 and 2 and at x=0 with duplicity 2

  40. cwrw238
    • 2 years ago
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    i meant -4

  41. cwrw238
    • 2 years ago
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    so we can write a(x+4)(x - 2)(x- 0)^2 or ax^2(x+4)(x-2)

  42. cwrw238
    • 2 years ago
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    can you continue from here?

  43. cwrw238
    • 2 years ago
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    you now need to use x = 5 y = -202.5

  44. Breno
    • 2 years ago
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    ive got 675 for a

  45. cwrw238
    • 2 years ago
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    -202.5 = 25a * 9 * 3 = -202.5 / (25*27)

  46. cwrw238
    • 2 years ago
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    cant be 675

  47. cwrw238
    • 2 years ago
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    -0.3?

  48. Breno
    • 2 years ago
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    oh ok

  49. cwrw238
    • 2 years ago
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    so you need to expand -0.3 x^2(x + 4\)(x - 2)

  50. Breno
    • 2 years ago
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    thanks

  51. cwrw238
    • 2 years ago
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    yw

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