Answer
a. $f(x) = -(x+3/2)^2 + 21/4$
b. See graph attached below
c. Maximum value = 21/4
Work Step by Step
$f(x) = -x^2 -3x + 3$
a. $f(x) = -( x^2 + 3x + 9/4) + 3 +9/4$
$f(x) = -(x+3/2)^2 + 21/4$
b. See graph attached below
c. The maximum value is at the vertex, which is at (-3/2, 21/4) (from standard form)
Maximum value = 21/4
