Respuesta :

bekkarmahdi702

Answer:

Step-by-step explanation:

  • F(x)= (x-2)(x-3)

This form is already factored so it can help us to find the intercepts with the x-axis

how ?

  • The intercepts with the x-axis are simply the points where f(x)=0

from the factored form we can deduce that x=2 and x=3 are the points that represent the intercepts with the x-axis since f(2)=0 and f(3)=0

  • The intercept with the y-axis is the image of 0 so f(0)=(0-2)(0-3)=6

so :

  • The intercepts with the x-axis are (2,0) and (3,0)
  • The intercept with they-axis is (0,6)

To get the standard form we should develop :

  • f(x)=x²-3x-2x+6

             = x²-5x+6

now the vertex form with the axis of symmetry :

  • There are many ways to do it but here is the simplest one :

the standard form is x²-5x+6 :

  • b= -5
  • a= 1
  • c= 6

The coordinates of the vertex are : ([tex]\frac{-b}{2a}[/tex],f([tex]\frac{-b}{2a}[/tex]) )

  • let A be the vertex : a([tex]\frac{5}{2}[/tex],[tex]\frac{-1}{4}[/tex])
  • the axis of simmetry is x= 5/2
  • The vertex form is : 1*(x-[tex]\frac{5}{2}[/tex])²/(1/4)

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