Without graphing, determine whether the equation has a graph that is symmetric with respect to the x-axis, the y axis, the origin, or none of these. y=x^2+13 Select all that apply. A. x-axis B. y-axis C. origin D. none of these

To determine the symmetry of the graph of the equation , we need to check for symmetry with respect to the x-axis, y-axis, and the origin.1. **Symmetry with respect to the x-axis:** - To test for symmetry with respect to the x-axis, we replace with and see if the equation remains unchanged. - Original equation: - Replace with : - This is not the same as the original equation, so the graph is not symmetric with respect to the x-axis.2. **Symmetry with respect to the y-axis:** - To test for symmetry with respect to the y-axis, we replace with and see if the equation remains unchanged. - Original equation: - Replace with : \( y = (-x)^2 + 13 \) - Since \( (-x)^2 = x^2 \), the equation remains unchanged: - Therefore, the graph is symmetric with respect to the y-axis.3. **Symmetry with respect to the origin:** - To test for symmetry with respect to the origin, we replace with and with and see if the equation remains unchanged. - Original equation: - Replace with and with : \( -y = (-x)^2 + 13 \) - Since \( (-x)^2 = x^2 \), the equation becomes: - This is not the same as the original equation, so the graph is not symmetric with respect to the origin.Based on this analysis, the correct answer is:B. y-axis