Answer
See graph
Work Step by Step
Given \begin{equation}
y \geq-\frac{1}{2}(x-8)^2+4.
\end{equation} The equation $$y=-\frac{1}{2}(x-8)^2+4$$ is an equation of a parabola in standard vertex form. Let's determine the vertex so that we can mark it on the graph. The coordinates $(h,k)$ of the vertex are found from the function: \begin{equation}
\begin{aligned}
y&=a(x-h)^2+k\\
h&=8\\
k&=4.
\end{aligned}
\end{equation} The graph of the function is shown in the figure below with the horizontal and vertical intercepts labelled. The vertex $(8,4)$ is also labelled.
The solution of the inequality is the set of points above and on the quadratic curve.
