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Thread: Issue with Converting to Standard Form

  1. #1
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    Issue with Converting to Standard Form

    I have this problem. Convert to standard form.

    -2x2-6x+10

    The answer I come up with does not work when I check my work. What did I do wrong?
    -2(x+1.5)2+14.5


    C-
    x

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  2. #2
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    Re: Issue with Converting to Standard Form

    It's hard to point out where you went wrong when we don't know what you actually did to get that answer...

    $\displaystyle \begin{align*} -2 \, x^2 - 6 \, x + 10 &= -2 \, \left( x^2 + 3 \, x - 5 \right) \\ &= -2 \, \left[ x^2 + 3\,x + \left( \frac{3}{2} \right) ^2 - \left( \frac{3}{2} \right) ^2 - 5 \right] \\ &= -2 \, \left[ \left( x + \frac{3}{2} \right) ^2 - \frac{9}{4} - \frac{20}{4} \right] \\ &= -2 \, \left[ \left( x + \frac{3}{2} \right) ^2 - \frac{29}{4} \right] \\ &= -2 \, \left( x + \frac{3}{2} \right) ^2 + \frac{29}{2} \end{align*}$

    I agree with your answer, why do you think it's wrong?
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    Re: Issue with Converting to Standard Form

    Quote Originally Posted by jennasam400 View Post
    I have this problem. Convert to standard form.

    -2x2-6x+10

    The answer I come up with does not work when I check my work. What did I do wrong?
    -2(x+1.5)2+14.5


    C-
    x

    your answer is correct.

    on expanding the answer you get

    $-2(x+1.5)^2+14.5$

    $=-2(x^2+2.25+1.5x)+14.5$

    $=-2x^2-4.5-3x+14.5$

    $=-2x^2-3x+10$

    This is the equation given in question.
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    Re: Issue with Converting to Standard Form

    Quote Originally Posted by deesuwalka View Post
    your answer is correct.

    on expanding the answer you get

    $-2(x+1.5)^2+14.5$

    $=-2(x^2+2.25+1.5x)+14.5$

    $=-2x^2-4.5-3x+14.5$

    $=-2x^2-3x+10$

    This is the equation given in question.
    No, you are incorrect.
    $(x+1.5)^2$ is not equal to $x^2+2.25+1.5x$, it is equal to $x^2+ 2.25+ 3.0x$.

    (I would have written it x^2+ 3.0x+ 2.25 : (x+ a)^2= x^2+ 2ax+ a^2 not x^2+ ax+ a^2.
    Last edited by topsquark; Jan 11th 2017 at 04:13 PM. Reason: Fixed up some LaTeX
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    Re: Issue with Converting to Standard Form

    Quote Originally Posted by jennasam400 View Post
    I have this problem. Convert to standard form.

    -2x2-6x+10
    The answer I come up with does not work when I check my work. What did I do wrong?
    -2(x+1.5)2+14.5
    I have a naive question. Who or what determines standard form?
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  6. #6
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    Re: Issue with Converting to Standard Form

    Quote Originally Posted by Plato View Post
    I have a naive question. Who or what determines standard form?
    From my experience, most secondary algebra texts have standard form as $y=ax^2+bx+c$. The same texts usually name $y=a(x-h)^2+k$ as the vertex form.

    I have seen the vertex form called standard form in other sources. I've also seen $y=ax^2+bx+c$ called the general form.

    Depends on the text, I guess.
    Thanks from Plato and topsquark
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    Re: Issue with Converting to Standard Form

    Quote Originally Posted by HallsofIvy View Post
    No, you are incorrect.
    $(x+1.5)^2$ is not equal to $x^2+2.25+1.5x$, it is equal to $x^2+ 2.25+ 3.0x$.

    (I would have written it x^2+ 3.0x+ 2.25 : (x+ a)^2= x^2+ 2ax+ a^2 not x^2+ ax+ a^2.
    Yes, I've mistakenly typed. thanks
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