Find the domain and range of $LaTeX: \displaystyle f(x)=- 4 \left(x - 8\right)^{2} - 9$

The domain of every polynomial is all real numbers. The sign of $LaTeX: \displaystyle a$ is negative so the function has a maximum value at the vertex. This gives the range as $LaTeX: \displaystyle (-\infty,-9]$