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Math Help - finding x-intercepts: EASY

  1. #1
    Member Mr Rayon's Avatar
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    finding x-intercepts: EASY

    Sketch the graphs the following function:

    f(x) = 10 + 3x -x^2

    I know how you would go about sketching this. You would first have to find the x and y-intercepts however, I am having trouble finding the x-intercepts.

    The thing is I've never factorised a quadratic where the leading, ax^2 is negative. Note: It's just the '-' in the x^2 that's confusing me. I've tried a few times with failure:

    -x^2 + 3x + 10 = 0
    -(x + 5)(x - 2) = 0

    however, I think it's supposed to be factorised to (5 -x)(2 + x)
    anyway, how would I go about contiuning to solve for the values of x for which the y values would equal 0? please outline each step slowly for me so I'll understand.

    Thank you.
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  2. #2
    Super Member Quacky's Avatar
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    Hiya,

    Both your initial answer, and the one you expected, were correct! They're the same thing written differently. But there is a much easier method.

    If you start at

    -x^2 + 3x + 10 = 0

    Now add x^2 to both sides:

    3x+10=x^2

    Now take away 3x from both sides:

    10=x^2-3x

    Now take away 10 from both sides:

    0=x^2-3x-10

    So if you just reverse all of the +/- signs, you'll get the same result for the intercepts. Isn't that much easier to factorize?
    Last edited by Quacky; February 10th 2010 at 12:51 PM.
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  3. #3
    Member Mr Rayon's Avatar
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    Quote Originally Posted by Quacky View Post
    So if you just reverse all of the +/- signs, you'll get the same result for the intercepts. Isn't that much easier to factorize?
    WOW, yeah thank you so much!
    ...it was so simple.
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  4. #4
    Master Of Puppets
    pickslides's Avatar
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    Quote Originally Posted by Quacky View Post

    -x^2 + 3x + 10 = 0

    So if you just reverse all of the +/- signs, you'll get the same result for the intercepts. Isn't that much easier to factorize?
    Easier again, just multiply both sides through by -1

    -1 \times (-x^2 + 3x + 10) = -1\times (0)

    x^2 - 3x - 10 = 0
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