Question

Given the functions f(x) = 3x2, g(x) = x2 − 4x + 5, and h(x) = –2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry.

Answer 1

f(x) = 3x²

`x = (-b)/(2a) = (-0)/(2(3)) = (0)/(6) = 0`
f(x) = 3x²
f(0) = 3(0)²
f(0) = 3(0)
f(0) = 0
(x, f(x)) = (0, 0)

g(x) = x² - 4x + 5

`x = (-b)/(2a) = (-(-4))/(2(1)) = (4)/(2) = 2`
g(x) = x² - 4x + 5
g(2) = (2)² - 4(2) + 5
g(2) = 4 - 8 + 5
g(2) = -4 + 5
g(2) = 1
(x, g(x)) = (2, 1)

h(x) = -2x² + 4x + 1

`x = (-b)/(2a) = (-4)/(2(-2)) = (-4)/(-4) = 1`
h(x) = -2x² + 4x + 1
h(1) = -2(1)² + 4(1) + 1
h(1) = -2(1) + 4 + 1
h(1) = -2 + 5
h(1) = 3
(x, h(x)) = (1, 3)