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)

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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)

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

3 is greater then both of those numbers