Let f(x)=-(x-1)^2+4
Solve f(x)=0 to find the x-intercepts
This function is symmetric about the line x = 1
Therefore the vertex is on that line.
It is a parabola opening up (holds water)
When x = 1, y = 4 so the vertex is at (1,4)
The curve never drops below y = 4 so never crosses the x axis
So the answer is zero.