Chapter 2 - Linear and Quadratic Functions - Section 2.4 Properties of Quadratic Functions - 2.4 Assess Your Understanding - Page 160: 101

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

Step 1. To test symmetry with respect to the x-axis, replace $(x,y)$ with $(x,-y)$ to get $(x)^2+4(-y)^2=16$ which is the same as the original equation, thus it is symmetric with respect to the x-axis. Step 2. To test symmetry with respect to the y-axis, replace $(x,y)$ with $(-x,y)$ to get $(-x)^2+4(y)^2=16$ which is the same as the original equation, thus it is symmetric with respect to the y-axis. Step 3. To test symmetry with respect to the origin, replace $(x,y)$ with $(-x,-y)$ to get $(-x)^2+4(-y)^2=16$ which is the same as the original equation, thus it is symmetric with respect to the origin.