Question

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

Answer 1

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)<h(x)<g(x)

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