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Math Help - Determine an equation for

  1. #1
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    Question Determine an equation for

    Determine an equation for the graph of the polynomial function shown...

    There's a graph that goes from x-axis: -2 to +2 and y-axis:+4 to -4.
    There are three zero's marked at: -1, 0, +2
    There is one point given at: (-1,-2)
    The graph starts from the bottom goes up towards -1(x-axis) then curves and goes through zero, down to the point (-1,-2), curves at that point and goes up through the point (2,0). The curves are consistent in size.


    So what I was thinking was something like:

    y = a (x+1)(x-2)^2
    or
    y = 1 (x+1)(x-2)^2
    ...This get's me somewhat close but is not correct.
    I know you need +1 and -2 in brackets, since these will be opposite of the zero's which are -1 and +2.


    __________________________________________________ _________________

    Sort of related so I though I'd ask in the same thread. This is a different question.
    Determine an equation in factored form for the polynomial function with zeros 2 (order2), 2/3, and 3 that passes through the point (1,6).

    What does "(Order 2)" mean? What are orders? I know zero's are where the graph hit's 0-on-the-x-axis. How would I start this question?
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  2. #2
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    Re: Determine an equation for

    Quote Originally Posted by tdotodot View Post
    Determine an equation for the graph of the polynomial function shown...

    There's a graph that goes from x-axis: -2 to +2 and y-axis:+4 to -4.
    I assume this only means that the area in which the graph is shown is -2< x< 2, -4< y< 4, not that the graph includes the points (-2, 4) and (2, -4)

    [quote]There are three zero's marked at: -1, 0, +2
    So we have (-1, 0), (0, 0), and (2, 0) which means, assuming this is a polynomial, we have factors of x+ 1, x, and x- 2.

    There is one point given at: (-1,-2)
    That's contradictory- you said above that was a 0 at -1 and if the graph of a function goes through (-1, 0) it cannot also go through (-1, -2).

    The graph starts from the bottom goes up towards -1(x-axis) then curves and goes through zero, down to the point (-1,-2), curves at that point and goes up through the point (2,0). The curves are consistent in size.


    So what I was thinking was something like:

    y = a (x+1)(x-2)^2
    or
    y = 1 (x+1)(x-2)^2
    ...This get's me somewhat close but is not correct.
    I know you need +1 and -2 in brackets, since these will be opposite of the zero's which are -1 and +2.
    This is impossible. If this is the graph of any function, it [b]cannot go through both (-1, 0) and (-1, -2).

    __________________________________________________ _________________

    Sort of related so I though I'd ask in the same thread. This is a different question.
    Determine an equation in factored form for the polynomial function with zeros 2 (order2), 2/3, and 3 that passes through the point (1,6).

    What does "(Order 2)" mean? What are orders? I know zero's are where the graph hit's 0-on-the-x-axis. How would I start this question?
    I suspect that "order of a zero" is defined in the text where you got this problem. A zero, a, of a polynomial is of "order n" if the polynomial has a factor of (x- a)^n.
    Saying that this polynomial function has "zeros 2 (order2), 2/3, and 3" means it is (at least) of the form [ex]y= a(x- 2)^2(x- 2/3)(x- 3)[tex]. Assuming there are no other factors you can determine a so that the graph "passes through the point (1,6)" by setting x= 1, y= 6 in that and solving for a.
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  3. #3
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    Re: Determine an equation for

    [QUOTE=HallsofIvy;796996]I assume this only means that the area in which the graph is shown is -2< x< 2, -4< y< 4, not that the graph includes the points (-2, 4) and (2, -4)

    There are three zero's marked at: -1, 0, +2
    So we have (-1, 0), (0, 0), and (2, 0) which means, assuming this is a polynomial, we have factors of x+ 1, x, and x- 2.


    That's contradictory- you said above that was a 0 at -1 and if the graph of a function goes through (-1, 0) it cannot also go through (-1, -2).


    This is impossible. If this is the graph of any function, it [b]cannot go through both (-1, 0) and (-1, -2).


    I suspect that "order of a zero" is defined in the text where you got this problem. A zero, a, of a polynomial is of "order n" if the polynomial has a factor of (x- a)^n.
    Saying that this polynomial function has "zeros 2 (order2), 2/3, and 3" means it is (at least) of the form [ex]y= a(x- 2)^2(x- 2/3)(x- 3)[tex]. Assuming there are no other factors you can determine a so that the graph "passes through the point (1,6)" by setting x= 1, y= 6 in that and solving for a.
    I might not have explain the graph (first question) in the best way. I took a pic and uploaded it so you can see the graph. The close up won't upload but that should be fine.
    Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting


    ____________________

    Second question, so pretty much what they mean by order is the exponent to the term? So zeros -3 (order3) and zero +535 (order34) would be -3^3 and 535^34 respectively?
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  4. #4
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    Re: Determine an equation for

    Quote Originally Posted by tdotodot View Post
    Determine an equation for the graph of the polynomial function shown...

    There's a graph that goes from x-axis: -2 to +2 and y-axis:+4 to -4.
    There are three zero's marked at: -1, 0, +2
    There is one point given at: (-1,-2)
    On the graph you now show that is (1, -2), not (-1, -2)!
    So this must be of the form y= a(x+ 1)x(x- 2). To find a, set x=1, y= -2 in that and solve for a.

    The graph starts from the bottom goes up towards -1(x-axis) then curves and goes through zero, down to the point (-1,-2), curves at that point and goes up through the point (2,0). The curves are consistent in size.


    So what I was thinking was something like:

    y = a (x+1)(x-2)^2
    or
    y = 1 (x+1)(x-2)^2
    ...This get's me somewhat close but is not correct.
    I know you need +1 and -2 in brackets, since these will be opposite of the zero's which are -1 and +2.


    __________________________________________________ _________________

    Sort of related so I though I'd ask in the same thread. This is a different question.
    Determine an equation in factored form for the polynomial function with zeros 2 (order2), 2/3, and 3 that passes through the point (1,6).

    What does "(Order 2)" mean? What are orders? I know zero's are where the graph hit's 0-on-the-x-axis. How would I start this question?
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  5. #5
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    Re: Determine an equation for

    Quote Originally Posted by tdotodot View Post
    Second question, so pretty much what they mean by order is the exponent to the term? So zeros -3 (order3) and zero +535 (order34) would be -3^3 and 535^34 respectively?
    No, that's not what I said. We are talking about polynomial functions not just numbers. If you are told that a polynomial function has a "zero of order 3 at -3 and a zero of order 34 at 535" then the polynomial has factors (x+3)^3(x- 535)^{34}, possibly with other factors.
    Thanks from topsquark
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