Question 998657
{{{y=-x^2+x+2}}}---------as given, lead term coefficient indicates concave downward, vertex a maximum.
{{{y=-(x^2-x-2)}}}
{{{y=-(x+1)(x-2)}}}
Roots will be  -1 and +2.  Symmetry axis in the exact middle.


{{{(-1+2)/2}}}
{{{1/2}}}
{{{highlight(x=1/2)}}}-----------Axis of Symmetry



Evaluate y at {{{x=1/2}}}.
{{{y=-(1/2+1)(1/2-2)}}}
{{{y=-(3/2)(-3/2)}}}
{{{highlight(y=9/4)}}}-------Vertex is  ( 1/2, 9/4 ).


RANGE
All real values so that {{{y<=9/4}}}, because remember, this graph has a vertex as a maximum.