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?

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Step-by-step explanation:

y = - (x + 1) ² + 1

Shift 1 unit to the right:

y = - (x + 1 - 1) ² + 1

y = - x² + 1

Shift 5 units down:

y = - x² + 1 - 5

y = - x² - 4

Rotate 180° about the vertex:

y = - (-x²) - 4

y = x² - 4

Find the zeros:

0 = x² - 4

x² = 4

x = - 2 or 2

Therefore, a = - 2 and b = 2, so b-a = 4.

Step-by-step explanation:

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