1. The problem asks us to determine if the function $p(x)$ is even, odd, or neither based on its graph. 2. Recall the definitions: - A function $f(x)$ is **even** if $f(-x) = f(x)$ for all $x$ in the domain. Graphically, even functions are symmetric about the $y$-axis. - A function $f(x)$ is **odd** if $f(-x) = -f(x)$ for all $x$ in the domain. Graphically, odd functions have rotational symmetry about the origin. 3. The graph described is a downward-opening parabola with vertex at $(0,6)$ and symmetric about the $y$-axis. 4. Since the graph is symmetric about the $y$-axis, it satisfies $p(-x) = p(x)$. 5. Therefore, $p(x)$ is an **even** function. Final answer: $p(x)$ is even.