Find the \( x \) - and \( y \)-intercepts. (If an answer does not exist, enter DNE.) \( x \)-intercept (smaller \( x \)-value) \( \quad(x, y)=( \) \( \square \) ) \( x \)-intercept (larger \( x \)-value) \( \quad(x, y)=( \) \( \square \) ) \( y \)-intercept \[ (x, y)=(\square) \] Test for symmetry. (Select all that apply.) The graph is symmetric with respect to the \( x \)-axis. The graph is symmetric with respect to the \( y \)-axis. The graph is symmetric with respect to the origin. The graph is not symmetric with respect to the \( x \)-axis, \( y \)-axis, or the origin.

To find the x-intercepts and y-intercepts, we typically set \( y = 0 \) for x-intercepts and \( x = 0 \) for y-intercepts. **X-intercepts**: Solve \( f(x) = 0 \). For example, if the function \( f(x) = ax^2 + bx + c \), you would factor or use the quadratic formula to find the x-values where the graph intersects the x-axis. Depending on the discriminant, you may find two real solutions, one real solution, or none (DNE). **Y-intercept**: Simply substitute \( x = 0 \) into the equation \( f(0) \). This gives you the point where the graph crosses the y-axis. For symmetry, check: - **x-axis symmetry**: If replacing \( y \) with \( -y \) gives the same equation, it's symmetric about the x-axis. - **y-axis symmetry**: If replacing \( x \) with \( -x \) yields the same equation, it's symmetric about the y-axis. - **Origin symmetry**: If replacing both \( x \) and \( y \) with their negatives results in the same equation, it has origin symmetry. If none of these hold, the graph is not symmetric with respect to any axis. Happy graphing!