Respuesta :
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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Answer:
To find the axis of symmetry.
A quadratic equation is in the form of :
[tex]ax^2+bx+c =0[/tex] where a, b and c are coefficients and x is the variable
Axis of symmetry is given by :
[tex]x = -\frac{b}{2a}[/tex]
First identify a, b and c in the equation
[tex]f(x) = 3x^2[/tex]
⇒ a= 3 , b= 0 and c =0
[tex]g(x) = x^2-4x+5[/tex]
⇒ a = 1 , b = -4 and c =5
and
[tex]h(x) = -2x^2+4x+1[/tex]
⇒ a = -2 , b =4 and c =1
Using above formula of the axis of symmetry:
[tex]x = -\frac{b}{2a}[/tex]
then;
In f(x)
Axis of symmetry: [tex]x = -\frac{0}{2 \cdot 3} = 0[/tex]
Similarly;
In g(x)
Axis of symmetry : [tex]x = -\frac{-4}{2 \cdot 1} = \frac{4}{2} =2[/tex]
In h(x)
Axis of symmetry : [tex]x = -\frac{4}{2 \cdot -2} = \frac{4}{4} =1[/tex]
Rank from least to greater on basis of axis of symmetry: 0 , 1 , 2
⇒ f(x); h(x) ; g(x)
