Question 6693
Since {{{-2x^2-x+4}}} can be computed for every x (unlike, say, square root, which can only be computed for positive x), the domain is the entire set of real numbers.

The range can be guessed by looking at the graph 

{{{graph( 300, 300, -5, 5, -10, 10, -2x^2-x+4) }}}

It has its maximum right in the middle between the roots, which is x = -b/2a, or {{{x= -(-1)/(2*(-2)) = -1/4}}}. Now use substitution of {{{x = -1/4}}} into expression {{{-2x^2-x+4}}}:

*[invoke substitution "-2x^2-x+4", "x", -0.25]

So, the domain is all numbers and the range is from minus infinity to 4.125.