hello :
the parabola's equation is : f(x) = a(x-1)²-9
the coefficient of the squared expression in the parabola's equation is : a
but ; f(0) = -6 ... ( y-intercepts (0,-6) )
-6 = a(0-1)²-9
-6 =a -9
a=3
f(x) = 3(x-1)²-9
the x-intercepts when : f(x) =0
3(x-1)²-9 =0
(x-1)² =3
x-1 = √3) or x-1 = -√3)
x= 1 +√3 or x= 1 -√3 are
the x-intercepts