which steps transform the graph of y=x^2 to y=-2(x-2)^2+2

1 answer

The steps to transform the graph of y = x^2 to y = -2(x-2)^2 + 2 are:

1. Reflect the graph vertically: Multiply the original equation by -1 to reflect the graph vertically. This changes y = x^2 to y = -x^2.

2. Stretch the graph vertically: Multiply the equation by a constant to stretch or compress the graph vertically. In this case, multiply y = -x^2 by -2 to stretch the graph vertically. The equation becomes y = -2x^2.

3. Move the graph horizontally: Add or subtract a value inside the parentheses to shift the graph horizontally. In this case, subtract 2 inside the parentheses to move the graph 2 units to the right. The equation becomes y = -2(x-2)^2.

4. Move the graph vertically: Add or subtract a value outside the parentheses to shift the graph vertically. In this case, add 2 outside the parentheses to move the graph 2 units up. The final equation becomes y = -2(x-2)^2 + 2.