Given the functions f(x) = x2 + 6x − 1, g(x) = –x2 + 2, and h(x) = 2x2 − 4x + 3, rank them from least to greatest based on their axis of symmetry.

Axis of symmetry = x = -b/2a
where y = ax² + bx + c

f(x) = x² + 6x - 1 ⇒ a = 1 ; b = 6 ; c = -1
x = -(6)/2(1) = -6/2 = -3

g(x) = -x² + 2 ⇒ a = -1 ; b = 0 ; c = 2
x = -0/2(-1) = 0/-2 = 0

h(x) = 2x² - 4x + 3 ⇒ a = 2 ; b = -4 ; c = 3
x = -(-4)/2(2) = 4/4 = 1

least :       f(x) = x² + 6x - 1    ; axis of symmetry is -3
middle :    g(x) = -x² + 2         ; axis of symmetry is 0
greatest :  h(x) = 2x² - 4x + 3 ; axis of symmetry is 1