Which steps transform the graph of
y•x^2 to y = -2(x - 2)^2 + 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
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 x-axis, stretch by the factor 2, and translate up 2 units
The correct answer is: Translate 2 units to the right, reflect across x-axis, stretch by the factor 2, and translate up 2 units.
To understand why this answer is correct, let's break down the transformation steps one by one:
1. Translate 2 units to the right: This means that every point on the graph will shift horizontally to the right by 2 units. In other words, we replace 'x' with '(x - 2)' in the equation.
2. Reflect across x-axis: This means that every point on the graph will flip vertically. We do this by changing the sign of 'y' in the equation, which reflects the graph across the x-axis.
3. Stretch by the factor 2: This means that the graph will become taller or narrower. We achieve this by multiplying the coefficient of the 'x^2' term by 2 in the equation. Therefore, the equation becomes 'y = -2(x - 2)^2'.
4. Translate up 2 units: This means that every point on the graph will shift vertically upwards by 2 units. In other words, we replace 'y' with '(y + 2)' in the equation.
By following these steps, we obtain the equation 'y = -2(x - 2)^2 + 2', which represents the transformation of the graph of 'y = x^2' according to the given sequence of steps.