Question

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

Answer 1

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.

Answer 2

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)

Answer 3

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...