# Precalculus

posted by Jason

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

1. drwls

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.

2. Damon

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)

3. Jason

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...

## Similar Questions

1. ### Algebra,Math, graphs help

This is what the directions state to do: (A) Complete the table,(B)describe the resulting graphs by identifying the vertex point, (c) the graph’s direction, (d) and any axis intercepts gleaned from the table or graph. Problem #1 …
2. ### math, algebra,graphs help

THe directions state: (A)Complete the table, (B) describe the resulting graphs by identifying the vertex point, (C)the graph’s direction, (D) and any axis intercepts gleaned from the table or graph Problem #3 Equation : y = 2x^2 …
3. ### Alegrba

Please check my answers. Also, can I see some graphs of y-axis symmetry, orgin of symmetry, or neither?
4. ### Algebra-Polynomails

Please explain to me orgin of symmetry, y-axis semmetry, or if its neither. 1. Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. f(x) = 4x^2 - x^3 -this is how I did it: f(x)=(-4x^2)-x^3,I …
5. ### Algebra II

Determine whether the grapg of the given equation is symmetric with respect to the x-axis, y-axis, and/or the orgin. f(x)=3x²+1 x²+y²=81
6. ### Precalculus

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
7. ### Precalculus

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 |x|+|y|=4
8. ### symmetry help

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 |x|+|y|=4
9. ### pre-cal

what is the slant asymptote of the graph of the rational function and b use the slant to graph the rational function. f(x)x^2-x-20/x-6 a. y=?