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.

The axis of symmetry is x=-b/2a

for f (x), the axis of symmetry is x=0, because there is no b.

when x=0, f (x) = 4*0²-1=-1, so the vertex is (0, - 1)

because a in this case is 4, a positive number, the parabola opens upward, - 1 is the lowest value.

for g (x), x = - (-8) / 2*1=4, f (x) = 4²-8*4+5=-11, the vertex is (4,-11)

because a is 1 in this case, a positive number, the parabola opens upward, - 11 is the lowest value.

for h (x), x = - (-12) / [2 * (-3) ]=-2, f (x) = - 3 * (-2) ²-12 (-2) + 1=13, the vertex is (-2,13)

because a is - 3 in this case, a negative number, 13 is the largest value.

f (x) 's is obviously larger than g (x) (the graph of f (x) is above that of g (x)), but for h (x), since it opens downward from y=13, it overwraps with part of f (x) and g (x), I'm not sure how you can compare that.

but if we look at the vertex alone, g (x) is the least, then f (x), then h (x) is the largest.

I hope all this makes sense.

The answer is actually A g (x) is the lowest amount, h (x) being the middle, and f (x) being the largest, I see where you were going with it, but I think you miscalculated f (x), because it is larger than h (x)

(I just took the test and got A right.)