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.

Answer 1

The answer is x = 0, 2, 3

Answer 2

If you have a quadratic equation y = ax² + bx + c
Where a, b, and c are constants.
The axis of symmetry is: x = -b/2a

For f(x) = 2x² - 8x, comparing a=2, b = -8, c = 0
x = -b/2a = -(-8)/(2*2) = 8/4 = 2. Axis of symmetry or line of symmetry is x = 2

For g(x) = x² - 6x +1, comparing a=1, b = -6, c = 1. (Note am taking the last term as +1, it still does not affect the answer if it is otherwise)
x = -b/2a = -(-6)/(2*1) = 6/2 = 3. Axis of symmetry or line of symmetry is x = 3

For h(x) = -2x² comparing a=-2, b = 0, c = 0
x = -b/2a = -(0)/(2*-2) = 0/-4 = 0. Axis of symmetry or line of symmetry is x = 0

Ranking the axis of symmetry or line of symmetry from the least to the greatest:

x = 0, 2 , 3 That is:

h(x), f(x), & g(x)