Question

How do you determine whether the graph of `y^2+3x=0` is symmetric with respect to the x axis, y axis or neither?

Answer 1

Equation is symmetric w.r.t. `x`-axis.

Explanation:

When a graph is symmetric w.r.t. `x`-axis, changing `y->-y` does not change the equation and when it symmetric w.r.t. `y`-axis, changing `x->-x` does not change the equation.

As the equation is `y^2+3x=0`, it is obvious that as `(-y)^2=y^2`, the equation remains as `y^2+3x=0` and hence equation is symmetric w.r.t. `x`-axis.

However, it is not symmetric w.r.t. `y`-axis as `x->-x` changes it to `y^2-3x=0`, which is a different equation.

graph{y^2+3x=0 [-15, 5, -5, 5]}