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Thread: Algebra 2 (Help me for the love of God!)

  1. #1 Algebra 2 (Help me for the love of God!) 
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    I need some help on about five questions... The first two I need to find a quadratic equation that has the give roots:
    The first question: 3/4, 9/2
    The second question: -0.25, 0.25

    Then next three I need to write each equation in the form f(x) = a(x-h)^2+k (unless it's not already in that form). I need to name the vertex, axis of symmetry, and direction of opening for the graph of eahc quadratic function. Then I need to graph it.
    The third question is: f(x)=a(x-5)^2-7
    The fourth question is: f(x)= -9^2+54x-8
    The fifth (and final) question is: f(x)=0.25x^2-6x-16

    Please Help!! :?


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  3. #2 Re: Algebra 2 (Help me for the love of God!) 
    Forum Radioactive Isotope mitchellmckain's Avatar
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    Quote Originally Posted by EAfreak
    I need some help on about five questions... The first two I need to find a quadratic equation that has the give roots:
    The first question: 3/4, 9/2
    The second question: -0.25, 0.25
    Simplicity itself: let me give you an example 4, -1.45
    I simply write (x-4)(x-(-1.45)) = 0
    now if x is 4 or -1.45 I get 0
    I can multiply this out using (a+b)(c+d)= ac+ad+bc+bd
    x^2 - 2.55 x - 5.8 = 0

    Quote Originally Posted by EAfreak
    Then next three I need to write each equation in the form f(x) = a(x-h)^2+k (unless it's not already in that form). I need to name the vertex, axis of symmetry, and direction of opening for the graph of eahc quadratic function. Then I need to graph it.
    The third question is: f(x)=a(x-5)^2-7
    The fourth question is: f(x)= -9^2+54x-8
    The fifth (and final) question is: f(x)=0.25x^2-6x-16

    Please Help!! :?
    Again an example: f(x)=x^2 - 2.55 x - 5.8
    The process is known as completing the square
    and it uses (a-b)^2 = a^2 -2ab + b^2
    where in our f(x), a^2 = x^2 and 2ab = 2.55 x
    This means that a=x and b = 2.55/2 = 1.275
    so (x-1.275)^2 = x^2 -2.55 x + 1.625625
    So we take or f(x) and add (x-1.275)^2 and subtract x^2 -2.55 x + 1.625625 to get (x-1.275)^2 -5.8 -1.625625
    Since what we added and subtracted are equal it is still f(x)
    So f(x) = (x-1.275)^2 - 7.425625

    SO the vertex of the parabola is at (1.275, -7.425625)
    The axis of symmetry is x = 1.275
    and the parabola opens upward because comparing
    f(x) = (x-1.275)^2 - 7.425625 to f(x) = a(x-h)^2+k
    we see that a = +1 which is positive


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  4. #3  
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    For a quadratic equation of the form x^2 + bx + c = 0
    The sum of its two roots is -b
    The product of its two roots is c.

    the first equation is:
    x^2 -(3/4 + 9/2) + (3/4)*(9/2) = 0
    x^2 - (21/4)x + 27/8 = 0
    8x^2 - 42x + 27 = 0

    The second equation is
    x^2 +(0.25 - 0.25)x +0.25*(-0.25) = 0
    x^2 - 1/16= 0
    16x^2 - 1 = 0

    ************************************************** *
    Write equations in the form f(x) = a(x-h)^2+k.

    The fourth equation:
    -9x^2+54x-8
    = -9(x^2 - 6x + 8/9)
    = -9[(x^2 - 6x + 9) - 9 + 8/9]
    = -9[(x - 3)^2 - 9 + 8/9]
    = -9(x - 3)^2 + 81 - 8
    = -9(x - 3)^2 + 73

    The fifth equation
    0.25x^2-6x-16
    = 0.25[x^2 - 24x - 64]
    = 0.25[(x^2 - 24x + 144) - 144 -64]
    = 0.25)[(x -12)^2 - 208]
    = 0.25(x - 12)^2 - 52
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  5. #4  
    Forum Professor serpicojr's Avatar
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    orca: On this forum, we prefer not to answer homework questions, but rather we attempt to help people by providing examples (as mitchellmckain did) or by asking leading questions. Of course, we're excited to have you on the math forum--just keep this in mind for the future!
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  6. #5  
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    I need Algebra/ Algebra 2 Help?

    imagery numbers

    i(2+i)


    (-3+7i)(1-2i)


    (3-2i)


    completing the square



    (7x+2)=110


    graph the equation


    y=-x-4x-1



    y > 2x+4x-1





    I have tried to do the problems up above but I always keep getting the wrong answer when I check in the back of the book. Please help me understand what I am doing wrong.


    Thank you
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