posted by Jason on .
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-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.
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)
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...