Answer
Local Maximum is y=1.25 when x = -0.5
Work Step by Step
The local maximum value of $g(x) = -x^2 - x +1$ can be determined from its vertex
Vertex = $\frac {-b}{2a} = \frac{1}{-2} = \frac{-1}{2}$
At x=-0.5, g(-0.5) =1.25
So the local maximum is y=1.25 when x = -0.5
