Question

Which phrase best describes the translation from the graph

y=(x-5 )² +7
to the graph of y=(x + 1)²-2?

1. 6 units left and 9 units down
2. 6 units right and 9 units down
3. 6 units left and 9 units up
4. 6 units right and 9 units up

Answer 1

A) 6 units left and 9 units down

Explanation:

Answer 2

Explanatory Answer:

The original equation of the graph is y=(x-5)²+7, which is in vertex form with vertex at (5, 7). This vertex represents the minimum point of the parabola.

The new equation is y=(x+1)²-2, which is also in vertex form with vertex at (-1, -2). This vertex represents the minimum point of the new parabola.

To transform the original graph to the new graph, we need to perform horizontal and vertical shifts of the vertex. Specifically, we need to shift the vertex 6 units to the right and 9 units up to get from (5, 7) to (-1, -2).

Therefore, the correct phrase to describe the translation from the original graph to the new graph is:

6 units right and 9 units up