which steps transform the graph of y=x^2 to y=-(x-3)^3+2
would it be 3 units to right translate up 2 units
almost.
translate right 3
(x-3)^3
reflect in x-axis
-(x-3)^3
translate up 2
-(x-3)^3+2
Yes, you are correct! To transform the graph of y = x^2 to y = -(x - 3)^3 + 2, you need to follow the following steps:
1. Horizontal Translation: To move the graph 3 units to the right, you will replace x with (x - 3). This shift is in the opposite direction of the sign, so instead of adding 3, we subtract 3 inside the parentheses.
2. Vertical Translation: To shift the graph up 2 units, you simply add 2 to the entire function. This will affect the y-coordinate of each point on the graph.
So, combining these steps, the transformation of the graph of y = x^2 to y = -(x - 3)^3 + 2 can be summarized as follows:
1. Replace x with (x - 3).
2. Add 2 to the entire function.
By applying these steps, you will indeed translate the graph 3 units to the right and 2 units up.