Take the derivative
g'(x) = 2x + 9
Min or max when g'(x) = 0
==> 2x+9 = 0 ==> 2x = -9 ==> x = -9/2
g"(x) = 2 > 0
so, this is a minimum
Find g(4.5) to determine the actual point.
or...
x^2 + 9x - 36
= x^2 + 9x + 81/4 - 81/4 - 36
= (x +9/2)^2 - 225/4
so vertex (minimum) at (-9/2, -225/4)
