Find the domain and range of $LaTeX: \displaystyle f(x)=- 5 x^{2} - 30 x - 57$

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. The vertex is located at $LaTeX: \displaystyle h=\frac{-b}{2a}=-3$ and $LaTeX: \displaystyle k=f(h)=-12$ . This gives the range as $LaTeX: \displaystyle (-\infty,-12]$