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
The correct answer is A. translate 2 units to the left, translate down 2 units, stretch by the factor 2.
To determine the steps that transform the graph of y = x^2 to y = –2(x – 2)^2 + 2, let's break down the equation:
1. The negative sign in front of the 2, -2(x - 2)^2, causes a reflection across the x-axis.
2. The (x - 2)^2 term indicates a translation of 2 units to the right.
3. The -2 term translates the graph vertically down by 2 units.
4. The +2 at the end translates the graph vertically up by 2 units.
Based on these steps, the correct transformation is option:
D. reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2.
The correct answer is D. reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2.
Explanation:
1. Reflecting across the x-axis changes the sign of the y-values, so the graph is flipped upside down.
2. Translating 2 units to the right means shifting all points on the graph 2 units to the right.
3. Translating up 2 units means shifting all points on the graph 2 units up.
4. Stretching by a factor of 2 means multiplying all the y-values by 2.
By applying these steps in the given sequence, the graph of y = x^2 is transformed into the graph of y = –2(x – 2)2 + 2.