Question

F(x) = (x - 2)(x - 3)

Answer 1

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 : ($\frac{-b}{2a}$,f($\frac{-b}{2a}$) )

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