Answer
symmetric with respect to the x-axis.
$(3,0)$, $(0,\pm3)$.
Work Step by Step
1. To test for x-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $3(x)+(-y)^2=9$ which is the same as the original, thus it is symmetric with respect to the x-axis.
2. To test for y-axis symmetry, replace $(x,y)$ with $(-x,y)$, we have $3(-x)+(y)^2=9$ which is different from the original, thus it is not symmetric with respect to the y-axis.
3. To test for origin symmetry, replace $(x,y)$ with $(-x,-y)$, we have $3(-x)+(-y)^2=9$ which is different from the original, thus it is not symmetric with respect to the origin.
4. To find the x-intercept, let $y=0$, we have $x=3$ or $(3,0)$. To find the y-intercept, let $x=0$, we have $y=\pm3$ or $(0,\pm3)$.
