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
$x = \frac{-b}{2a} = \frac{-0}{2(3)} = \frac{0}{6} = 0$
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
$x = \frac{-b}{2a} = \frac{-(-4)}{2(1)} = \frac{4}{2} = 2$
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
$x = \frac{-b}{2a} = \frac{-4}{2(-2)} = \frac{-4}{-4} = 1$
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)