Precalculus

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find any intercepts of the graph of the given equation. determine whether the graph of the equation possesses symmetry with respect to the x-axis, y-axis, or orgin

y=x^2-2x-2

  • Precalculus -

    y = (x-1)^2 -3

    When y = 0, (x-1)^2 = 3
    x - 1 = + or - sqrt3
    x = 1 + sqrt3 or 1 - sqrt3

    When x = 0, y = -3

    There is no symmetry about the x or y axes, or origin.

  • Precalculus -

    When x = 0, y = -2, y axis intercept

    When y = 0
    x = [ 2 +/- sqrt(4+8)]/2 = 1 +/- sqrt 3

    therefore parabola is symmetric about the vertical line x = 1

    show it by completing the square

    x^2 - 2x = y + 2

    x^2 - 2x + 1 = y+3

    (x-1)^2 = (y+3)
    vertex at (1,-3)

  • Precalculus -

    thank you damon! that was exactly what i was looking for, by the way it's 4:32 am here and i've been searching for that answer for hours...

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