How do u test for the symmetry of a linear equation algebraically?

Question

for example y=x^2 - 2

Answer 1

y = x² - 2 is not linear, it's quadratic.

it's symmetric over the y axis because changing the value of x to -x will not change the value of y.

if f(-x) = f(x), symmetry around y axis, even function.

if f(-x) = -f(x), symmetry around origin, odd function.

Answer 2

to test for symmetry you find the vertex of equation

to find the vertex (h.k)=((=b/2a),f(-b/2a)) symmetry is from the x axis