Find the domain and range of $LaTeX: \displaystyle f(x)=2 x^{2} + 32 x + 142$

The domain of every polynomial is all real numbers. The sign of $LaTeX: \displaystyle a$ is positive so the function has a minimum value at the vertex. The vertex is located at $LaTeX: \displaystyle h=\frac{-b}{2a}=-8$ and $LaTeX: \displaystyle k=f(h)=14$ . This gives the range as $LaTeX: \displaystyle [14,\infty)$