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anonymous

  • 5 years ago

can anyone help with solving problems using quadratic functions?

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  1. amistre64
    • 5 years ago
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    perhaps, whatcha need?

  2. anonymous
    • 5 years ago
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    The company discovered that it costs $30 to produce 2 widgets, $118 to produce 4 widgets, and $766 to produce 10. Using the quadratic function, find the cost of producing 6 widgets.

  3. amistre64
    • 5 years ago
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    when you are given 3 points, you need to do what looks like a reverse quadratic.... lets determine the points for our graph: (2,30) (4,118) (10,766).. ok?

  4. amistre64
    • 5 years ago
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    now we want a curve to match these numbers, so we need to find the "coefficients" of a quadratic equation to solve it... Ax^2 +Bx +C = y

  5. amistre64
    • 5 years ago
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    we know our x's and y's so the ABC becomes our "unknown" variables..backwards I know...

  6. amistre64
    • 5 years ago
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    lets form 3 equations and then make them all equal like this: (2)^2A +(2)B + C = 30 (4)^2A +(4)B + C = 118 (10)^2A +(10)B + C = 766

  7. amistre64
    • 5 years ago
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    4a +2b +c = 30 16a + 4b +c = 118 100a +10b +c = 766

  8. amistre64
    • 5 years ago
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    lets solve this system of equation :) what yor poison, substitution, elimination, or matrix?

  9. anonymous
    • 5 years ago
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    what you mean?

  10. amistre64
    • 5 years ago
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    if you dont know what I mean by now, then you are nor ready to solve this..... a system of equations is where you have 3 equations and want to know where they all have common points. We do that by either substitution techniques, elimination techniques or a matrix technique

  11. amistre64
    • 5 years ago
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    well....2 or more equations with points in common :)

  12. anonymous
    • 5 years ago
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    well in the lesson for this assignment it never said anything about any of those.

  13. amistre64
    • 5 years ago
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    we could try linear equations, but i gotta tell you, it says to do it with q quadratic....

  14. anonymous
    • 5 years ago
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    well the lesson is called "solving equations with quadratic functions"

  15. amistre64
    • 5 years ago
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    right, and since they gave you 3 points and no equation, we have to find the equation using those points. We need to solve the 3 equations for a b and c in order to "find" the quadratic equation we need. otherwise, its just a shot in the dark :)

  16. amistre64
    • 5 years ago
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    Ill do substitution, it tends to be the most intuative of the methods...takes longer, but is eaiser to follow 4a +2b +c = 30 16a + 4b +c = 118 100a +10b +c = 766

  17. amistre64
    • 5 years ago
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    4a +2b +c = 30 solve for "c" c = -4a -2b + 30 we can use this "value" in the other two equations like this: 16a + 4b +(-4a - 2b +30) = 118 16a -4a +4b -2b = 118 -30

  18. amistre64
    • 5 years ago
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    12a +2b = 88 solve for another variable with this: b = -12a/2 +88/2

  19. amistre64
    • 5 years ago
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    use the c "value" in the other equation to get rid of that variable in it like we did to this one: 100a +10b +(-4a -2b +30) = 766 100a -4a +10b -2b = 766 - 30 106a +8b = 736 use the "b" value in this equation to solve for "a"

  20. amistre64
    • 5 years ago
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    106a +8(-6a +44) = 736 106a -48a +352 = 736 58a = 384 a = 384/58 ...reduce as needed we have a solid value for "a" now we can use it to find a solid value for "b"

  21. amistre64
    • 5 years ago
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    b = -6(384/58) +44 what does b = ??

  22. amistre64
    • 5 years ago
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    b = -1152/29 +44 ..... use this in your a value in your top most equation to find the value for c

  23. amistre64
    • 5 years ago
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    and as long as I did my math right, it should give you your a b and c values for your quadratic equation ;)

  24. amistre64
    • 5 years ago
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    100-4 is not 106.....

  25. radar
    • 5 years ago
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    Would you then substitute 6 in the newly found equation to find the cost of production?

  26. amistre64
    • 5 years ago
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    yes you would, and that would give you your answer.

  27. amistre64
    • 5 years ago
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    as long as I did all the math right.... 106 should be 96 96a -48a +352 = 736 48a = 384 a = 384/48 ...reduce as needed

  28. amistre64
    • 5 years ago
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    a = 8...much better ;)

  29. amistre64
    • 5 years ago
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    b = -6(8) +44 b = -48 + 44 = -4 a = 8, b = -4

  30. amistre64
    • 5 years ago
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    c = -4(8) -2(-4) + 30 c = -32 +8 +30 c = -2+8 = 6 your equation is then: 8x^2 -4x +6

  31. amistre64
    • 5 years ago
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    8(6)^2-4(6) +6 = your answer

  32. amistre64
    • 5 years ago
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    you can double check the ABC by plugging in t your point information and seeing if it is the same :)

  33. radar
    • 5 years ago
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    I think this company is having a heck of a learning curve!

  34. amistre64
    • 5 years ago
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    lol ..... the company in the eqample, or openstudy, or racergirlk? :)

  35. radar
    • 5 years ago
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    lol whew that was work. cul

  36. anonymous
    • 5 years ago
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    Thanks amistre64. would you be willing to help with the 4 i have left?

  37. amistre64
    • 5 years ago
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    what!?!?!! ..... maybe later tonight, I have classes in an hour ;)

  38. anonymous
    • 5 years ago
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    well thanks for the help

  39. radar
    • 5 years ago
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    I substituted the 2, 4, and 10 and obtained the amount of production cost as the problem stated. That is the correct answer, 6 widgets will cost $270, the company would be better off making only 2 widgets per production run!! LOL

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