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.
