Question 1119726
Range easier to identify if the equation is put into "vertex" form.  Domain will be all real numbers, since all polynomial functions have all real numbers as their domain.


{{{y=-x^2-x+8}}}
{{{-(x^2+x-8)}}}
{{{-(x^2+x+1/4-1/4-8)}}}
{{{-((x+1/2)^2-8&1/4)}}}
{{{-(x+1/2)^2+8&1/4}}}
and now you see??  Identify the MAXIMUM possible y value?



The form derived lets you see the vertex which is the maximum point for the parabola equation.  Domain for this parabola is x is all real numbers; and range is the real numbers less than and equal to {{{8&1/4}}}.  The parabola is concave downward.