Answer: b and d
Step-by-step explanation:
Since the roots are x=2 and x=6, we can write the equation as
[tex]f(x)=a(x-2)(x-6)[/tex]
Substituting in the coordinates of the vertex,
[tex]-4=a(4-2)(4-6)\\\\-4=a(2)(-2)\\\\-4=-4a\\\\a=1[/tex]
So, the equation is [tex]f(x)=(x-2)(x-6)[/tex].
On expanding, we get [tex]f(x)=x^2 - 8x+12[/tex]
