Show that  $f(x)=x^2$ is an even function and its graph is symmetric with respect to the y-axis.

Note that  $f(-x)={(-x)}^2=x^2.$ Thus,  $f(x)=f(-x).$ This implies that the function  $f(x)$ is even. Its graph is shown below. Observe that it is symmetric with respect to the y-axis.