Question

Given the functions f(x) = 4x2 - 1, g(x) = x2 - 8x + 5, and h(x) = -3x2 - 12x + 1, rank them from least to greatest based on their axis of symmetry. (2 points)

Answer 1

The axis of symmetry for a parabola in the form of f(x) = a(x - h)^2 + k is x = h.

For f(x) = 4x^2 - 1, the axis of symmetry is x = 0.

For g(x) = x^2 - 8x + 5, the axis of symmetry is x = 4.

For h(x) = -3x^2 - 12x + 1, the axis of symmetry is x = -4/3

So, the ranking from least to greatest based on their axis of symmetry would be:

h(x) = -3x^2 - 12x + 1 with x = -4/3

g(x) = x^2 - 8x + 5 with x = 4

f(x) = 4x^2 - 1 with x = 0