Question

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?

Answer 1

Explanation:

45

Answer 2

4

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.