The graph of the parabola defined by the equation y=-(x+1)^2+1 is shifted 1 unit to the right, then shifted 5 units down, then rotated 180 degrees about its vertex. The resulting parabola has zeros at x=a and x=b, where b≥a. What is b-a?
The vertex of this parabola is (-1, 1). When you shift it 1 unit to the right and 5 units down, the vertex is now (-1+1, 1-5), which is (0, -4). So now our parabola equation is y=-(x)^2-4
Rotating it 180 degrees means flipping it upside down (so if it was facing downwards, now it's facing upwards, and vice versa). We know our parabola is now facing downward because its there's a negative sign in the original equation.
If its now facing upward, then its positive. y=x^2-4
Zeroes are when y=0. x^2-4=0
x^2 = 4
x = +2, -2
Since b≥a, we know that b=2, and a=-2.