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= -5a= 1c= 6
The coordinates of the vertex are : (
,f(
) )
let A be the vertex : a(
![\frac{5}{2}](/tpl/images/0702/5551/21af6.png)
,
![\frac{-1}{4}](/tpl/images/0702/5551/bea8c.png)
)the axis of simmetry is x= 5/2 The vertex form is : 1*(x-
![\frac{5}{2}](/tpl/images/0702/5551/21af6.png)
)²/(1/4)