Given functions f (x) = 3x^2, g (x) = x^2-4x+5, and h (x) = - 2x^2+4x+1

Rank them from least to greatest

Ok, ranked by axis of symmetry

basically x=something is the axis of symmetry

the way to find the axis of symmetry is to convert to vertex form and find h and that's the axis of symmetry

but there's an easier way

for f (x) = ax^2+bx+c

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

nice hack my teacher taught me

so

f (x) = 3x^2+0x+0

axis of symmetry is - 0 / (3*2), so x=0 is the axis of symmetry for f (x)

g (x) = 1x^2-4x+5,

axis of symmetry is - (-4) / (2*1) = 4/2=2, x=2 is axis of symmetry for g (x)

h (x) = - 2x^2+4x+1

axis of symmetry is - 4 / (2*-2) = - 4/-4=1, x=1 is the axis of symmetry for h (x)

0<1<2

axisies

f (x)
order based on their axises of symmetry is f (x), h (x), g (x)