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

1 Answer
Dec 12, 2017

Answer:

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]}