Which of the following statements about f(x)=(x-4)^2-1 are true? select all that apply

We have that
f(x)=(x-4)^2-1  in the question and f(x)=-(x-4)^2-1 in the picture
so

I'm going to analyze the two cases

using a graph tool

case 1)
f(x)=(x-4)^2-1
the vertex is the point (4,-1)
the x intercepts are the points (3,0) and (5,0)
the y intercept is the point (0,15)
the axis of symmetry is x=4
see the attached figure N 1 

case 2)
f(x)=-(x-4)^2-1
the vertex is the point (4,-1)
there is no x intercepts
the y intercept is the point (0,-17)
the axis of symmetry is x=4
see the attached figure N 2

the answer 
considering the case N 2 is
vertex (4,-1)------> is correct
y intercept  (0,-17)-----> is correct
axis of symmetry x=4-----> is correct

Both the vertex being (4, -1) and the y-intercept being (0, 17) are true.

We can tell the vertex portion given the formula of a graph in vertex form: f(x) = (x - h) + k, where (h, k) is the vertex. This will show us that (4, -1) is the vertex.

We also know that the y intercept is -17 because when we plug 0 into the equation, we get -17.
f(x) = -(x - 4)^2 - 1
f(x) = -(-4)^2 - 1
f(x) = -16 - 1
f(x) = -17.

The x-intercept option is not true because the vertex is below the x axis and the negative coefficient gives the graph a downward trend. Therefore, there will be no x-intercept.