Chapter 3 - Linear and Quadratic Functions - 3.3 Quadratic Functions and Their Properties - 3.3 Assess Your Understanding - Page 148: 101

symmetric with respect to the x-axis, the y-axis, and the origin.

Step 1. To test x-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $(x)^2+4(-y)^2=16$ and there is no change in the equation, thus it is symmetric with respect to the x-axis. Step 2. To test y-axis symmetry, replace $(x,y)$ with $(-x,y)$, we have $(-x)^2+4(y)^2=16$ and there is no change in the equation, thus it is symmetric with respect to the y-axis. Step 3. To test origin symmetry, replace $(x,y)$ with $(-x,-y)$, we have $(-x)^2+4(-y)^2=16$ and there is no change in the equation, thus it is symmetric with respect to the origin.