Find the x-intercepts of the parabola with vertex (1,-19)and y-intercept (0,-18).

Hello : 
f(x) = a(x-1)² -19
find : a
f(0) = -18
-18 = a(0-1)² -19
-18 = a -19
a = 1 
f(x) = (x-1)²-19
x-intercepts of the parabola when : f(x) = 0
(x-1)²-19 =0
(x-1)²=19
x-1 =√19  or x-1 =√19
x = 1+√19    or x = 1-√19 are x-intercepts of the parabola