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Math Help - Graphs And Quadratics

  1. #1
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    Graphs And Quadratics

    7. The diagram shows the graphs of y = x2 x, y = x + 2, y = 8 and y = -2x + 4.



    Use the graphs to find the solutions to:

    (a) x2 x = 0

    (b) x2 x = x + 2

    (c) x2 x = 8

    (d) x2 x = -2x + 4

    (e) x2 x 8 = 0

    (f) x2 + x = 4

    Im not sure how to read off this kind of graph. Help please. How exactly do I find soloutions from this graph? Please be detailed as I need to answer all these questions.
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  2. #2
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    Hi there

    for  x^2 - x = 0 you need to find graphically where  y = x^2 - x cuts the x-axis. It seems to cut through the points x = 0,1

    With the next question you have to consider where  y= x^2 - x and  y = x + 2 intersect each other.

    They do not intersectat a value that is clearly defined on your graph but you can conclude that the solution lies on  x \in (-1,0)\cap(2,3)

    To get exact values in can solve this kind of equations using a little algebra, solve for x


     x^2 - x = x + 2

    moving everything to one side

     x^2 - 2x -2 = 0

    then completing the square

    Completing the square - Wikipedia, the free encyclopedia

     (x^2 - 2x +(\frac{-2}{2})^2 )-2-1= 0

     (x - 1)^2 -3 = 0

     x = \pm\sqrt{3}+1

     x \approx -0.7,2.7
    Last edited by pickslides; April 27th 2009 at 03:45 PM. Reason: typo
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  3. #3
    Member rtblue's Avatar
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    nicely done, pickslides. As a matter of fact, we were doing completing the square in my algebra I class today, but it was more advanced. We had to complete the square, to get it from:

    ax^2+by^2+cx+dy+e=0 by the way, this is the standard equation of a circle.

    then, we completed the square twice, to make it:

    (x-h)^2+(y-k)^2=r^2 this is the center-radius form, in a circle. h is the x value of the radius. k is the y value of the radius. r is the radius of the circle. x and y are any given point that the circle touches.
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  4. #4
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    Hi.

    e.) X^2 - x - 8 =0

    f.) x^2 + x = 4

    are the only two I am stuck on. Need help!
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  5. #5
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    Quote Originally Posted by Sailee316 View Post
    Hi.

    e.) X^2 - x - 8 =0

    f.) x^2 + x = 4

    are the only two I am stuck on. Need help!

    Are we trying to sketch these functions or just solve for x?


    If you want to sketch the functions then I would complete the square which turns the function into turning point form.

     x^2-x-8

    Take the middle terms coeffecient, half it, then square it. This gives you a new 3rd term.

     (x^2-x +(\frac{-1}{2})^2)-8-(\frac{-1}{2})^2)

    simplifying this

     (x^2-x +\frac{1}{4})-8-\frac{1}{4}

    factoring the expression inside the bracket gives

     (x-\frac{1}{2})^2-\frac{33}{4}

    This function is

     y =x^2

    moved to the right \frac{1}{2} and down  \frac{33}{4}
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  6. #6
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    Quote Originally Posted by pickslides View Post
    Are we trying to sketch these functions or just solve for x?


    If you want to sketch the functions then I would complete the square which turns the function into turning point form.

     x^2-x-8

    Take the middle terms coeffecient, half it, then square it. This gives you a new 3rd term.

     (x^2-x +(\frac{-1}{2})^2)-8-(\frac{-1}{2})^2)

    simplifying this

     (x^2-x +\frac{1}{4})-8-\frac{1}{4}

    factoring the expression inside the bracket gives

     (x-\frac{1}{2})^2-\frac{33}{4}

    This function is

     y =x^2

    moved to the right \frac{1}{2} and down  \frac{33}{4}
    UPDATE: I have spoken to my teacher and he says I have to extrapolate to find the interception points for the two questions. I think this means move x^2 - x down to -8 and read off where they intercept. If the line of x^2 -x passes through the line twice I must write down two sets of x and y coordinates. Still need help with these two. Thanks
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  7. #7
    No one in Particular VonNemo19's Avatar
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    Sailee! Do you have a handle on this thing yet? If not, let me know!
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  8. #8
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    Quote Originally Posted by Sailee316 View Post
    7. The diagram shows the graphs of y = x2 x, y = x + 2, y = 8 and y = -2x + 4.







    Use the graphs to find the solutions to:

    (a) x2 x = 0

    (b) x2 x = x + 2

    (c) x2 x = 8

    (d) x2 x = -2x + 4

    (e) x2 x 8 = 0

    (f) x2 + x = 4

    Im not sure how to read off this kind of graph. Help please. How exactly do I find soloutions from this graph? Please be detailed as I need to answer all these questions.
    Duplicate questions: http://www.mathhelpforum.com/math-he...-graphs-2.html

    Thread closed.
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