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Math Help - Writing a function in standard form

  1. #1
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    Writing a function in standard form

    Express the function 'f' in standard form:
    -2x^2 - 6x + 3

    I've got:
    (-2x^2 - 6x/2 + 36/4) + 3
    (-2x^2 - 3x + 9) + 3
    -2(x^2 - 3x/-2 + 9/-2) + 3 - (9/-2)
    = y=(x + 3/2)^2 + 15/2

    I inputted the original function and the standard form into a graphing calculator and it came up with two different parabolas. Did I make an error in my math?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by SquawkVFR View Post
    Express the function 'f' in standard form:
    -2x^2 - 6x + 3

    I've got:
    (-2x^2 - 6x/2 + 36/4) + 3
    (-2x^2 - 3x + 9) + 3
    -2(x^2 - 3x/-2 + 9/-2) + 3 - (9/-2)
    = y=(x + 3/2)^2 + 15/2

    I inputted the original function and the standard form into a graphing calculator and it came up with two different parabolas. Did I make an error in my math?
    Okay, there are some notational problems going on here. This is the way I would recommend doing this.

    \displaystyle -2x^2 - 3x + 3

    \displaystyle (-2x^2 - 3x) + 3

    \displaystyle -2 \left ( x^2 + \frac{3}{2} x \right ) + 3

    \displaystyle -2 \left ( x^2 + \frac{3}{2} x + \left [ \frac{9}{4} \right ] -  \left [ \frac{9}{4} \right ] \right ) + 3

    \displaystyle -2 \left ( x^2 + \frac{3}{2} x + \left [ \frac{9}{4} \right ]  \right ) -  (-2) \cdot \left [ \frac{9}{4} \right ] + 3

    \displaystyle -2 \left ( x + \frac{3}{2} \right ) ^2 + \frac{15}{2}

    -Dan
    Last edited by topsquark; February 28th 2011 at 03:05 PM.
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