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

Dec 12, 2017

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

#### Explanation:

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

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

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

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