1. **State the problem:** We need to graph the function $f(x) = -(x - 3)^2$ and plot the vertex and another point on the parabola. 2. **Identify the vertex:** The function is in vertex form $f(x) = a(x - h)^2 + k$ where $(h, k)$ is the vertex. Here, $a = -1$, $h = 3$, and $k = 0$, so the vertex is at $(3, 0)$. 3. **Plot the vertex:** The vertex is the highest point because $a = -1 < 0$, so the parabola opens downward. 4. **Find another point:** Choose a value of $x$ near the vertex, for example $x = 4$. Calculate $f(4) = -(4 - 3)^2 = -(1)^2 = -1$. So another point is $(4, -1)$. 5. **Graph shape:** The parabola opens downward with vertex at $(3, 0)$ and passes through $(4, -1)$. This confirms the shape and position of the parabola on the Cartesian grid. **Final answer:** Vertex at $(3, 0)$ and another point at $(4, -1)$ on the parabola $f(x) = -(x - 3)^2$.