Without graphing, determine whether the following 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-x+2 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**: For a graph to be symmetric about the x-axis, replacing with should yield an equivalent equation. Let's test this: Replace with : This is not equivalent to the original equation . Therefore, the graph is **not** symmetric about the x-axis.2. **Symmetry with respect to the y-axis**: For a graph to be symmetric about the y-axis, replacing with should yield an equivalent equation. Let's test this: Replace with : This is not equivalent to the original equation . Therefore, the graph is **not** symmetric about the y-axis.3. **Symmetry with respect to the origin**: For a graph to be symmetric about the origin, replacing with and with should yield an equivalent equation. Let's test this: Replace with and with : This is not equivalent to the original equation . Therefore, the graph is **not** symmetric about the origin.Since the graph is not symmetric with respect to the x-axis, y-axis, or the origin, the correct answer is:D. none of these