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Math Help - Finding x- and y-intercepts of a parabola.

  1. #1
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    Finding x- and y-intercepts of a parabola.

    I am asked to use algebra to find the x and y intercepts from the following equation;

    y = - x^2 + 3x + 8
    2

    Note; - x^2 above means - x^2 and - 2, I can't get the minus sign in the right place.

    Am I working along the right lines here;

    2y = - 2x^2 + 3x + 8
    2y = x^2 + 8
    y = x^2 + 8 - 2
    y = x^2 + 6

    I am not really sure I have understood the question?
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  2. #2
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    Re: Using algebra to find intercepts

    Y intercept is where the graph of a function intersect y axis. X intercept is where the graph of the function intersects the x axis.

    To find y intercept(s) of a function, substitue x = 0 and solve for y and you get y intercept.

    Similarly, to find x intercept(s), substitute y=0 and solve for x.

    Some times you get no solution (a contradiction), which means there is no x or y intercept for that function.
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  3. #3
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    Finding x- and y-intercepts of a parabola.

    OK so I think I am learning slowly without software

    I am looking for the x and y intercepts using algebra, so here I go;

    y = - x^2 + 3x + 8
    divide 2

    as previous, the - is belonging to both the x^2 and the division 2

    I think I first get rid of the division 2

    2y = - 2x^2 + 3x + 8
    y = x + 6

    when x = 0

    y = 6

    Finding the x intercept

    when y = 0

    0 = - 2x^2 + 3x + 8
    0 = -2x(x - 6x) + 8
    (x - 3) or (x + 4)

    So the intercepts are;

    + 3 and - 4

    Not 100% confident but how am I doing

    Thanks

    David
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  4. #4
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    Re: Finding x- and y-intercepts of a parabola.

    Quote Originally Posted by David Green View Post
    OK so I think I am learning slowly without software

    I am looking for the x and y intercepts using algebra, so here I go;

    y = - x^2 + 3x + 8
    divide 2

    as previous, the - is belonging to both the x^2 and the division 2

    I think I first get rid of the division 2

    2y = - 2x^2 + 3x + 8
    y = x + 6

    when x = 0

    y = 6

    Finding the x intercept

    when y = 0

    0 = - 2x^2 + 3x + 8
    0 = -2x(x - 6x) + 8
    (x - 3) or (x + 4)

    So the intercepts are;

    + 3 and - 4

    Not 100% confident but how am I doing

    Thanks

    David
    If the equation is y = \frac{-x^2}{2} + 3x + 8 then the y-intercept is trivial: Substitute x = 0 and get y = 8. I cannot fathom how you get y = 6.

    To get the x-intercepts, substitute y = 0:

    0 = \frac{-x^2}{2} + 3x + 8

    Multiply both sides by 2: 0 = -x^2 + 6x + 16.

    At this stage you can use the quadratic formula to solve for x. Alternatively:

    Multiply both sides by -1: 0 = x^2 - 6x - 16 \Rightarrow 0 = (x - 8)(x + 2). The solution for x is trivial.

    Sorry to say this, but you need to get urgent help with basic algebra from your teacher.
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  5. #5
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    Re: Finding x- and y-intercepts of a parabola.

    Quote Originally Posted by David Green View Post
    OK so I think I am learning slowly without software

    I am looking for the x and y intercepts using algebra, so here I go;

    y = - x^2 + 3x + 8
    divide 2
    Please don't do that. Either learn latex or, if you insist on plain text y = -(x^2)/2 + 3x + 8 or y = (-x^2+3x+8)/2


    I'm not sure what you've done between

    y = - x^2 + 3x + 8
    divide 2
    and


    2y = - 2x^2 + 3x + 8
    y = x + 6
    Exactly how did your +8 become a +6?
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  6. #6
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    Re: Finding x- and y-intercepts of a parabola.

    Quote Originally Posted by David Green View Post
    I am asked to use algebra to find the x and y intercepts from the following equation;

    y = - x^2 + 3x + 8
    2

    Note; - x^2 above means - x^2 and - 2, I can't get the minus sign in the right place.

    Am I working along the right lines here;

    2y = - 2x^2 + 3x + 8
    2y = x^2 + 8 Mr F says: Nothing here makes sense. What has happened to the 3x in the previous line ...?? Why is the coefficient of x^2 not -2 anymore. Why wasn't the 8 multiplied by 2 as well. Your effort is admirable but you have serious troubles which need to be addressed by your teacher in 1-on-1 help.

    y = x^2 + 8 - 2
    y = x^2 + 6

    I am not really sure I have understood the question?
    ..
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