91Ó°ÊÓ

We have given the following equation :-

$y=x^4-3x^2-4$.

We have to check the symmetry of this equation with respect to x-axis, y-axis and the origin.

The given equation is :-

$y=x^4-3x^2-4$.

We know that a graph is symmetrical about x-axis, if a point $\left(x,y\right)$lies on graph, then $\left(x,-y\right)$is also lies on graph.

So to check symmetry about x-axis, change $y$by $-y$in the given equation, then we have :-

$-y=x^4-3x^2-4$.

This equation is not same as the given equation.

So we can conclude that the given equation is not symmetric about x-axis.

The given equation is :-

$y=x^4-3x^2-4$.

We know that a graph is symmetrical about y-axis, if a point localid="1646238747871" $\left(x,y\right)$lies on graph, then localid="1646239323087" $\left(-x,y\right)$is also lies on graph.

So to check symmetry about y-axis, change $x$by $-x$in the given equation, then we have :-

localid="1646239307706" $$\begin{gathered} y={\left(-x\right)}^4-3{(-x)}^2-4 \\ ⇒y=x^4-3x^2-4 \end{gathered}$$

The resulting equation is same as the given equation.

So we can say that the given equation is symmetric about y-axis.

The given equation is :-

$y=x^4-3x^2-4$.

We know that a graph is symmetrical about origin, if a point $\left(x,y\right)$lies on graph, then $\left(-x,-y\right)$is also lies on graph.

So to check symmetry about origin, change $x$by $-x$and role="math" localid="1646239048720" $y$by role="math" localid="1646239074424" $-y$in the given equation, then we have :-

role="math" $$\begin{gathered} -y={\left(-x\right)}^4-3{(-x)}^2-4 \\ ⇒-y=x^4-3x^2-4 \end{gathered}$$

The resulting equation is not same as the given equation.

So we can say that the given equation is not symmetric about origin.