Final answer:
The correct translation from the graph y = (x - 5)^2 + 7 to y = (x + 1)^2 – 2 is 6 units right and 9 units down, based on the changes in the equation coefficients.
Step-by-step explanation:
The phrase that best describes the translation from the graph y = (x - 5)^2 + 7 to the graph of y = (x + 1)^2 – 2 is 6 units right and 9 units down.
To determine this, we examine the changes in the horizontal and vertical shifts represented by the between the equations of the two parabolas.
The horizontal shift is observed by comparing the -5 in the first equation to the +1 in the second equation. This represents a shift to the right by 6 units, since we're going from negative to positive.
The vertical shift is determined by the change from +7 to -2, which corresponds to moving 9 units downwards.