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)

QUESTION POSTED AT 02/06/2020 - 01:18 AM

Answered by admin AT 02/06/2020 - 01:18 AM

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)
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