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Math Help - quadratic function problems :'(

  1. #1
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    Question quadratic function problems :'(

    Kindly help me about this quadratic equation please

    Q: The quadratic function which takes the value 41 at x=-2 and the value 20 at x=5 and is minimized at x=2 is

    y = __x2 - __x + __

    The minimum value of this function is __


    I really need to solve this . thank you
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  2. #2
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    Re: quadratic function problems :'(

    Let y = ax^2 + bx + c for some unknown a, b and c. Write the given conditions as equations in a, b and c. You'll get three equations in three variables. Recall that the point of minimum of a parabola is -b / (2a).
    Thanks from Ruun
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  3. #3
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    Re: quadratic function problems :'(

    that will be the equation but i don't get how to compute it. I'm sorry I'm totally clueless
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  4. #4
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    Re: quadratic function problems :'(

    Quote Originally Posted by pauliana View Post
    that will be the equation
    What will be the equation?

    Quote Originally Posted by pauliana View Post
    but i don't get how to compute it.
    You don't compute an equation; you solve it.

    Start by substituting x = -2 into ax^2 + bx + c = 41. Similarly, substitute x = 5 into ax^2 + bx + c = 20. Finally, write the equation saying that the point of minimum, i.e., x = -b / (2a), equals 2.
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  5. #5
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    Re: quadratic function problems :'(

    a(-2)^2 + b(-2) + c = 41 = -4a - 2b + c = 41

    a(5)^2 + b(5) + c = 20 = 25a + 5b + c = 20


    is this correct?
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  6. #6
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    Re: quadratic function problems :'(

    Correct except that (-2)^2 = 4 and not -4. Negative times negative gives positive. Now you need the third equation, and then you can solve the resulting system of equations.
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  7. #7
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    Re: quadratic function problems :'(

    it this right?


    4a - 2b + c = 41
    25a + 5b + c = 20
    ____________________
    29a - 3b + 2c = 61
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  8. #8
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    Re: quadratic function problems :'(

    Quote Originally Posted by pauliana View Post
    it this right?


    4a - 2b + c = 41
    25a + 5b + c = 20
    ____________________
    29a - 3b + 2c = 61
    No, 5b - 2b = 3b, not -3b. Also, you don't gain anything by adding the equations because the resulting equation still has all three variables. It would be better to subtract the equations; then c would be eliminated.

    Quote Originally Posted by emakarov View Post
    Now you need the third equation, and then you can solve the resulting system of equations.
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  9. #9
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    Re: quadratic function problems :'(

    4a - 2b + c = 41
    - 25a + 5b + c = 20
    _____________________
    -21a + 3b =21

    right?
    wait how about The minimum value of this function is ___ ?
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  10. #10
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    Re: quadratic function problems :'(

    Quote Originally Posted by pauliana View Post
    4a - 2b + c = 41
    - 25a + 5b + c = 20
    _____________________
    -21a + 3b =21
    Hmm, no. The minus in the second equation looks like it acts on 25a only. In any case, -2b - 5b = -7b, so the result should be -21a -7b = 21. You can divide both sides by 7.

    Quote Originally Posted by pauliana View Post
    wait how about The minimum value of this function is ___ ?
    I have already said this.

    Quote Originally Posted by emakarov View Post
    Recall that the point of minimum of a parabola is -b / (2a).
    Quote Originally Posted by emakarov View Post
    Finally, write the equation saying that the point of minimum, i.e., x = -b / (2a), equals 2.
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  11. #11
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    Re: quadratic function problems :'(

    7 [-21a -7b = 21] 7 will be -3a = 7

    then

    x = -b
    ______ = 2
    2a


    I'm so sorry I'm lost again
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  12. #12
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    Re: quadratic function problems :'(

    I found the answer sheet for this question and it says

    y = 3x^2 - 12x + 5

    then the value of D = -7

    I don't get it
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  13. #13
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    Re: quadratic function problems :'(

    First, it is better to avoid notation spanning several lines because this forum does not preserve alignment. Instead of x=\frac{-b}{2a}=2, you can simply write x = -b / (2a) = 2.

    I don't understand the notation "7 [-21a -7b = 21] 7". Dividing -21a - 7b = 21 by 7 gives -3a - b = 3. The last equation, -b / (2a) = 2, can be multiplied by 2a to get -b = 4a, or 4a + b = 0. Thus, you have

    \begin{align*}-3a - b &= 3\\4a + b &= 0\end{align*}

    Adding these equations gives a = 3. Substituting this value of a into either of the two equations above gives you b, and knowing a and b you can find c from any of the equations in post #5 (with the correction in post #6).
    Thanks from pauliana
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  14. #14
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    Re: quadratic function problems :'(

    Quote Originally Posted by pauliana View Post
    I found the answer sheet for this question and it says

    y = 3x^2 - 12x + 5

    then the value of D = -7

    I don't get it
    The minimum value D of this quadratic function is the value at the point of minimum (see the end of post #10).
    Thanks from pauliana
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  15. #15
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    Re: quadratic function problems :'(

    oh I see I get it now . I do apologize for all the repeated question it just that I totally forget how to solve quadratic functions and the parabola itself

    thank you very very much
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