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.) translate 2 units to the right, reflect across the x-axis, stretch by the factor 2, and translate up 2 units
The correct answer is D.) 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:
A.) translate 2 units to the left, translate down 2 units, stretch by the factor 2.
To determine which steps transform the graph of y = x^2 to y = -2(x-2)^2 + 2, we need to analyze the changes that occur.
The original equation, y = x^2, represents a basic parabola. Here are the steps to transform the graph from y = x^2 to y = -2(x-2)^2 + 2:
1) Translation: The expression (x - 2) in (x - 2)^2 suggests a horizontal translation by 2 units to the right. The graph is shifted to the right by 2 units.
2) Reflection: The coefficient -2 before the expression (x - 2)^2 indicates a vertical reflection about the x-axis. The graph is reflected downwards.
3) Stretching: The coefficient -2 outside the squared expression indicates a vertical stretch by a factor of 2. The graph is stretched vertically.
4) Translation: The constant term +2 added at the end of the equation corresponds to a vertical translation by 2 units upward. The graph is shifted upwards.
Comparing the steps above with the given options:
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.) translate 2 units to the right, reflect across the x-axis, stretch by the factor 2, and translate up 2 units
The correct option is D.) translate 2 units to the right, reflect across the x-axis, stretch by the factor 2, and translate up 2 units.