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Clarence

  • one year ago

"Assume that the graph of the polynomial p(x)=ax2+bx+cpasses through the point (−1,2)and has a horizontal tangent at (12,−9). Find the sum a+b+c." I've already substitute (-1, 2) into the polynomial equation to get a - b + c = 2 and differentiate the original polynomial to get 2ax+b=0 and replaced x with 12 to get 24a + b = 0 as well as utilizing (12, -9) to get 144a + 12 b + c = -9 but I have no idea where to go from there..

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  1. asnaseer
    • one year ago
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    your steps are correct so far

  2. asnaseer
    • one year ago
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    you now have 3 equations with 3 unknowns

  3. asnaseer
    • one year ago
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    solve these to find a, b and c and then calculate a+b+c

  4. clarence
    • one year ago
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    I've tried to use row operations but was unsuccessful, is there a particular order that I should place these equations?

  5. asnaseer
    • one year ago
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    You could just use simple substitution, e.g. start by eliminating c using the last equation

  6. clarence
    • one year ago
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    I'm not quite sure I understand you, use 144a + 12b + c = -9 to eliminate c?

  7. asnaseer
    • one year ago
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    c = -9 -12b -144a from that equation now substitute this into your first equation

  8. clarence
    • one year ago
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    Oh, the a-b+c=2 equation?

  9. asnaseer
    • one year ago
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    yes :)

  10. asnaseer
    • one year ago
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    you will then be left with 2 equations in two unknowns - a and b

  11. clarence
    • one year ago
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    How does that help? I have -13b-143a=11 right now.

  12. asnaseer
    • one year ago
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    and you also have: 24a + b = 0

  13. asnaseer
    • one year ago
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    which gives you: b = -24a substitute that into: -13b-143a=11 and solve for a

  14. anonymous
    • one year ago
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    ok what do you need help with, solving for a?

  15. clarence
    • one year ago
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    a would equal 2/169?

  16. asnaseer
    • one year ago
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    not quite - you must have made a simple algebraic mistake

  17. clarence
    • one year ago
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    Did you not get 312a-143a=2?

  18. anonymous
    • one year ago
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    -13b-143a=11 -13(-24a) - 143 a = 11 312a - 143a = 11 169a = 11 /169 on both sides a = 11/169

  19. asnaseer
    • one year ago
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    remember the negative sign

  20. anonymous
    • one year ago
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    me? It went away

  21. asnaseer
    • one year ago
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    I am talking to @Clarence

  22. anonymous
    • one year ago
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    ok sorry just trying to help

  23. clarence
    • one year ago
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    So b = - 264/169?

  24. asnaseer
    • one year ago
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    yes :)

  25. anonymous
    • one year ago
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    good job!!

  26. asnaseer
    • one year ago
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    now you are just left with c to calculate and then you can work out what a+b+c equals

  27. clarence
    • one year ago
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    c being 63/169?

  28. asnaseer
    • one year ago
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    yup :)

  29. anonymous
    • one year ago
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    wow sounds like you got it down, now just add them together

  30. clarence
    • one year ago
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    So all together it'd be -190/169?

  31. asnaseer
    • one year ago
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    yes - well done! :)

  32. anonymous
    • one year ago
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    correct awesome job

  33. clarence
    • one year ago
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    Oh I get it now, thanks!

  34. asnaseer
    • one year ago
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    why do I feel like there is an echo in here :)

  35. clarence
    • one year ago
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    Probably because there is ;) Thanks again guys/girls!

  36. anonymous
    • one year ago
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    haha you keep typing and replying right before i do and i don't see it sorry

  37. clarence
    • one year ago
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    Aha, all good :)

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