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

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)

Read more on -

To find the axis of symmetry.

A quadratic equation is in the form of :

where a, b and c are coefficients and x is the variable

Axis of symmetry is given by :

First identify a, b and c in the equation

⇒ a= 3 , b= 0 and c =0

⇒ a = 1 , b = -4 and c =5

and

⇒ a = -2 , b =4 and c =1

Using above formula of the axis of symmetry:

then;

In f(x)

Axis of symmetry:

Similarly;

In g(x)

Axis of symmetry :  

In h(x)

Axis of symmetry :  

Rank from least to greater on basis of axis of symmetry: 0 , 1 , 2

⇒ f(x); h(x) ; g(x)

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐