Question

Given the functions f(x) = 2x2 - 8x, g(x) = x2 - 6x + 1, and h(x) = -2x2, rank them from least to greatest based on their axis of symmetry. (2 points)

A. g(x), f(x), h(x)

B. f(x), g(x), h(x)

C. h(x), f(x), g(x)

D. h(x), g(x), f(x)

Answer 1

C: h, f, g

Explanation:

The axis of symmetry of the standard form quadratic y=ax²+bx+c is given by the equation x=-b/(2a).

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The axes of symmetry for your functions are ...

f: x = -(-8)/(2(2)) = 8/4 = 2

g: x = -(-6)/(2(1)) = 6/2 = 3

h: x = -0/(2(-2)) = 0/4 = 0

From least to greatest, the order is h(x), f(x), g(x).

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Additional comment

The axis of symmetry is the vertical line through the vertex (minimum or maximum).