Which steps transform the graph of y = x2 to y = –2(x – 2)2 + 2?
(1 point)
Responses
translate 2 units to the left, translate down 2 units, stretch by the factor 2
translate 2 units to the left, translate down 2 units, stretch by the factor 2
translate 2 units to the right, translate up 2 units, stretch by the factor 2
translate 2 units to the right, translate up 2 units, stretch by the factor 2
reflect across the x-axis, translate 2 units to the left, translate down 2 units, stretch by the factor 2
reflect across the x -axis, translate 2 units to the left, translate down 2 units, stretch by the factor 2
translate 2 units to the right, reflect across the x-axis, stretch by the factor 2, and translate up 2 units
translate 2 units to the right, reflect across the x-axis, stretch by the factor 2, and translate up 2 units
The correct steps to transform the graph of y = x^2 to y = –2(x – 2)^2 + 2 are:
1. Translate 2 units to the right.
2. Reflect the graph across the x-axis.
3. Stretch the graph by the factor of 2.
4. Translate the graph up by 2 units.
To transform the graph of y = x^2 to y = -2(x - 2)^2 + 2, we need to follow these steps:
1. Translate 2 units to the right: This means we shift the entire graph horizontally to the right by 2 units.
2. Reflect across the x-axis: This means we flip the graph upside down, reflecting it across the x-axis.
3. Stretch by the factor 2: This means we stretch the graph vertically by a factor of 2. In this case, the stretching occurs after the reflection, which means the graph will be stretched upwards.
4. Translate up 2 units: This means we shift the entire graph vertically upwards by 2 units.
Therefore, the correct answer is: translate 2 units to the right, reflect across the x-axis, stretch by the factor 2, and translate up 2 units.