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Math Help - Parabola in Standard Form

  1. #1
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    Parabola in Standard Form

    Write f(x) = -x^2 + 6x - 4 in the standard form for a parabola.

    I came up with (x - 3)^2 + 5 but the right answer is
    -(x - 3)^2 + 5.

    Why must we place the minus infront of the quantity
    (x - 3) in this case?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    Write f(x) = -x^2 + 6x - 4 in the standard form for a parabola.

    I came up with (x - 3)^2 + 5 but the right answer is
    -(x - 3)^2 + 5.

    Why must we place the minus infront of the quantity
    (x - 3) in this case?
    Hello Magentarita,

    If you expand and simplify what you thought was the right answer, you would see quickly that your result would not match the original function.

    Standard form (vertex form) here is

    f(x)=a(x-h)^2+k

    You have:

    f(x)=-x^2+6x-4 which can be converted to:

    f(x)=-1(x^2-6x)-4 by factoring out -1.

    Complete the square.

    f(x)=-1(x^2-6x+9)-4+9

    f(x)=-(x-3)^2+5

    The vertex is at (3, 5) and the parabola opens downward because a < 0. We can't lose the negative because it was part of your original function.

    f(x)=ax^2+bx+c
    f(x)=-x^2+6x-4



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  3. #3
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    ok but.............

    Quote Originally Posted by masters View Post
    Hello Magentarita,

    If you expand and simplify what you thought was the right answer, you would see quickly that your result would not match the original function.

    Standard form (vertex form) here is

    f(x)=a(x-h)^2+k

    You have:

    f(x)=-x^2+6x-4 which can be converted to:

    f(x)=-1(x^2-6x)-4 by factoring out -1.

    Complete the square.

    f(x)=-1(x^2-6x+9)-4+9

    f(x)=-(x-3)^2+5

    The vertex is at (3, 5) and the parabola opens downward because a < 0. We can't lose the negative because it was part of your original function.

    f(x)=ax^2+bx+c
    f(x)=-x^2+6x-4


    I don't understand why we must factor out -1.
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  4. #4
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    Quote Originally Posted by magentarita View Post
    I don't understand why we must factor out -1.
    Because to complete the square, the x^2 coefficient is always 1, not -1.
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  5. #5
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    yes, I..........

    Quote Originally Posted by Prove It View Post
    Because to complete the square, the x^2 coefficient is always 1, not -1.
    Yes, I forgot about that rule for completing the square.
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