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.

A. f(x), g(x), h(x)
B. f(x), h(x), g(x)
C. g(x), h(x), f(x)
D. g(x), f(x), h(x)

Answer 1

A standard form for the equation of a parabola with vertex at (h,k) is
f(x) = a(x - h)² + k

By determining the vertex of the given parabolas, we can rank their symmetry from least to greatest on the basis of increasing values of h.

Consider f(x) = 3x².
f(x) = 3(x - 0)^2 + 0
h = 0

Consider g(x) = x² - 4x + 5
g(x) = (x - 2)² - 4 + 5 = (x - 2)² + 1
h = 2

Consider h(x) = -2x² + 4x + 1
h(x) = -2[x² - 2x] + 1
       = -2[(x - 1)² - 1] + 1
       = -2(x - 1)² + 3
h = 1

Answer: f(x), h(x), g(x)