Graph the function. \[ f(x)=-3 x^{2} \]

To graph the function \( f(x) = -3x^2 \), start by recognizing that it represents a downward-opening parabola due to the negative coefficient in front of the \( x^2 \). The vertex of the parabola is at the origin (0,0), and as x moves away from 0, the function decreases rapidly, since the value of \( -3x^2 \) becomes increasingly negative. Plot points such as \( (-1, -3), (1, -3), (-2, -12), (2, -12) \) to help visualize the parabola’s shape. Now, for the axis of symmetry, it’s located at \( x = 0 \). Don't forget to label your axes appropriately, and shade below the curve to indicate that the function values of \( f(x) \) are all negative for all real x, creating a clear and engaging graph that showcases the characteristics of this quadratic function!