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Math Help - Quadratic Equations and Forms

  1. #1
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    Quadratic Equations and Forms

    If I have a relation in Vertex form, how do I make it into standard form?

    y = a(x-h)^2 + k into y = ax^2 + bx +c

    Example questions:
    a) y = 5(x+3)^2 -2
    b) y = 2x(5-2x)+7


    I'm not exactly looking for the answers, I just want to understand HOW to solve these.

    Please help!


    ----------------------

    heres my solution to question a, if you could advise me that would be much appreciated!

    y = 5(x+3)^2 -2
    = 5(x^2+9x-9)-2
    = 5(x^2+9x)-2+9
    = 5x^2 + 9x + 7
    Last edited by Namis9; December 12th 2006 at 10:26 AM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Namis9 View Post
    If I have a relation in Vertex form, how do I make it into standard form?

    y = a(x-h)^2 + k into y = ax^2 + bx +c

    Example questions:
    a) y = 5(x+3)^2 -2
    b) y = 2x(5-2x)+7


    I'm not exactly looking for the answers, I just want to understand HOW to solve these.

    Please help!


    ----------------------

    heres my solution to question a, if you could advise me that would be much appreciated!

    y = 5(x+3)^2 -2
    = 5(x^2+9x-9)-2
    = 5(x^2+9x)-2+9
    = 5x^2 + 9x + 7
    You have the method, but some mistakes in your work:
    y = 5(x+3)^2 -2

    y = 5(x^2 + 6x + 9) - 2

    y = 5x^2 + 30x + 45 - 2

    y = 5x^2 + 30x + 43

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    You have the method, but some mistakes in your work:
    y = 5(x+3)^2 -2

    y = 5(x^2 + 6x + 9) - 2

    y = 5x^2 + 30x + 45 - 2

    y = 5x^2 + 30x + 43

    -Dan
    Thanks, I now understand what I did wrong. Much Appreciated!

    For the second question, where you are not squaring the brackets I am a little confused. Perhaps you can help me as well? I'm not even exactly sure where to start on this.

    y = 2x(5-2x)+7 into y=ax^2 + bx + c
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Namis9 View Post
    Thanks, I now understand what I did wrong. Much Appreciated!

    For the second question, where you are not squaring the brackets I am a little confused. Perhaps you can help me as well? I'm not even exactly sure where to start on this.

    y = 2x(5-2x)+7 into y=ax^2 + bx + c
    Sorry, I didn't realize you hadn't spotted what you are trying to do.

    All you are up do in this sort of thing is expanding the quadratic into its separate terms.

    In this case just multiply it out:
    y = 2x(5-2x)+7

    y = 10x - 4x^2 + 7

    y = -4x^2 + 10x + 7

    This is far easier than taking y = ax^2 + bx + c and going to y = a(x - h)^2 + k. All you need to do is expand out all the terms and simplify.

    -Dan
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  5. #5
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    Thank you very much

    You've helped me a lot.
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