which phrase best describes the translation from the graph ( y=(x - 5)^2+7 ) to the graph of ( y=(x + 1)^2-2…

which phrase best describes the translation from the graph ( y=(x - 5)^2+7 ) to the graph of ( y=(x + 1)^2-2 )?\n6 units left and 9 units down\n6 units right and 9 units down\n6 units left and 9 units up\n6 units right and 9 units up

which phrase best describes the translation from the graph ( y=(x - 5)^2+7 ) to the graph of ( y=(x + 1)^2-2 )?\n6 units left and 9 units down\n6 units right and 9 units down\n6 units left and 9 units up\n6 units right and 9 units up

Answer

Explanation:

Step1: Identify vertex form of parabola

The vertex form of a parabola is (y = a(x - h)^2 + k), where ((h,k)) is the vertex. For (y=(x - 5)^2+7), the vertex is ((5,7)). For (y=(x + 1)^2-2), the vertex is ((-1,-2)).

Step2: Calculate horizontal and vertical changes

Horizontal change: (x) - coordinate changes from (5) to (-1). The change is (-1-5=-6) (6 units left). Vertical change: (y) - coordinate changes from (7) to (-2). The change is (-2 - 7=-9) (9 units down).

Answer:

6 units left and 9 units down.