Question

What is the domain and range of the quadratic equation y = -2x^2 - 32x - 126?

Answer 1

domain unless otherwise specified is all real numbers

Answer 2

range is
\[(-\infty, 2]\]

Answer 3

this is a parabola that opens down, so the range will be from negative infinity to the maximum, which is the second coordinate of the vertex.
first coordinate of the vertex is
\[-\frac{b}{2a}=-\frac{-32}{2\times -2}=-8\] and if you replace x by -8 you get
\[y=2\] so that is the max