Question

Which steps transform the graph of y = x^2 to y = -2(x-2)^2 + 2? (1 point)

A. translate 2 units to the left, translate down 2 units, stretch by the factor 2

B. translate 2 units to the right, translate up 2 units, stretch by the factor 2

C. reflect across the x-axis, translate 2 units to the left, translate down 2 units, stretch by the factor 2

D. reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2

Answer 1

The correct answer is D.

To transform the graph of y = x^2 to y = -2(x-2)^2 + 2, the following steps need to be taken:

1. Reflect across the x-axis: This will change the sign of y, so the graph will now be y = -x^2.

2. Translate 2 units to the right: This means that the graph will be shifted horizontally to the right by 2 units, resulting in y = -(x-2)^2.

3. Translate up 2 units: This means that the graph will be shifted vertically upwards by 2 units, resulting in y = -(x-2)^2 + 2.

4. Stretch by the factor 2: This means that the graph will be vertically stretched by a factor of 2, resulting in y = -2(x-2)^2 + 2.

Therefore, the correct steps to transform the graph of y = x^2 to y = -2(x-2)^2 + 2 are to reflect across the x-axis, translate 2 units to the right, translate up 2 units, and finally stretch by the factor 2, which is answer D.