Question

f(x) = x2 + 2x - 9

Answer 1

complete the square ...

f(x) = x^2 + 2x <b<+ 1 - 1 - 9
= (x+1)^2 - 10

vertex of this upwards opening parabola is (-1,-1)
so the minimum is -10 when x = -1

or , using Calculus...

f ' (x) = 2x+2
= 0 for max/min
2x = -2
x = -1
f(-1) = 1 - 2 - 9 = -10
min is -10 , when x = -1