which phrase best describes the translation from the graph y = (x - 5)^2 + 7 to the graph of y = (x + 1)^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
Answer
Explanation:
Step1: Analyze x - coordinate change
For the vertex - form of a parabola (y=a(x - h)^2+k), the vertex of (y=(x - 5)^2+7) is ((5,7)) and the vertex of (y=(x + 1)^2-2) is ((-1,-2)). The change in the x - coordinate is (\Delta x=-1 - 5=-6). A negative change in the x - coordinate means a shift to the left.
Step2: Analyze y - coordinate change
The change in the y - coordinate is (\Delta y=-2 - 7=-9). A negative change in the y - coordinate means a shift downwards.
Answer:
6 units left and 9 units down