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Math Help - expanding binomials

  1. #1
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    expanding binomials

    Promise no more questions today! ^_^

    The reason I'm stuck on these is because I've completely forgotten what im doing, after returning to these from months ago.

    I need to:

    1) Express x^2 - 8x + 15 in the form (x + a )^2 + b where "a" and "b" are the numbers to be found.

    This is what I've got thus far:

    y = x^2 - 8x + 15

    = (x - 4 )^2 - (4)^2 + 15 = 0

    (x - 4)^2 - 16 + 15

    Then I need to plot for the original equation. Not alot

    2) Expand the following using Pascal's Triangle

    (2 + x)^3

    I could manage the (x+1)^n expansion but not sure how to go about this one.

    Thanks
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  2. #2
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    Hello,

    Quote Originally Posted by Nick87 View Post
    Promise no more questions today! ^_^

    The reason I'm stuck on these is because I've completely forgotten what im doing, after returning to these from months ago.

    I need to:

    1) Express x^2 - 8x + 15 in the form (x + a )^2 + b where "a" and "b" are the numbers to be found.

    This is what I've got thus far:

    y = x^2 - 8x + 15

    = (x - 4 )^2 - (4)^2 + 15 = 0

    (x - 4)^2 - 16 + 15

    Then I need to plot for the original equation. Not alot
    Sorry if I misunderstood what you've said, but you got it

    2) Expand the following using Pascal's Triangle

    (2 + x)^3

    I could manage the (x+1)^n expansion but not sure how to go about this one.

    Thanks
    So you know the formula for (x+1)^n

    It's the same for (2+x)^3

    =C(3,0) 2^0 x^3+C(3,1)2^1 x^2+C(3,2) 2^2 x^1+C(3,3) 2^3 x^0

    Where C(n,p)={p \choose n}
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  3. #3
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    So for the first one a=4 and b=-16?

    It says to use my answer to sketch the graph of y = x^2 - 8x + 15 so what does that mean? Can't I just draw the graph like usual?
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  4. #4
    Moo
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    Quote Originally Posted by Nick87 View Post
    So for the first one a=4 and b=-16?

    It says to use my answer to sketch the graph of y = x^2 - 8x + 15 so what does that mean? Can't I just draw the graph like usual?
    Erm...

    y=(x-4)^2-16+15=(x-4)^2-1

    --> a=-4 and b=-1

    To graph the thing, represent yourself :

    - you know how to graph y=x
    - imagine that if you add a certain number to x, it's like translating to the right or the left the graph
    - adding a constant (here, b) is like increasing or decreasing the curve, that is to say "go up or go down", because you add b to the ordinate of each point
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  5. #5
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    Quote Originally Posted by Moo View Post
    Erm...

    y=(x-4)^2-16+15=(x-4)^2-1

    --> a=-4 and b=-1
    *Slaps self* of course its -1!

    So what I need to do now is plot the orignal graph but with the translation {a \choose b}?
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  6. #6
    Moo
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    Quote Originally Posted by Nick87 View Post
    *Slaps self* of course its -1!

    So what I need to do now is plot the orignal graph but with the translation {a \choose b}?
    Yep !
    I have an hesitation, perhaps it's -a. Check on the graph which one it is
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  7. #7
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    Thank you so much for all your help!
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