Answer
a. $f(x) = -(x+1/2)^2 + 5/4$
b. See graph attached below
c. Maximum value = 5/4
Work Step by Step
$f(x) = -x^2 -x + 1$
a. $f(x) = -( x^2 + x + 1/4) + 1 +1/4$
$f(x) = -(x+1/2)^2 + 5/4$
b. See graph attached below
c. The maximum value is at the vertex, which is at (-1/2, 5/4) (from standard form)
Maximum value = 5/4
