1. First I sketched the basic function which was y=x^2 also known as the parent function. It is drawn with the color black.
2. Then I did a vertical translation by moving six units up the y-axis resulting in the equation y=x^2+6. The graph of this equation is in red.
3. Next I did a horizontal translation by moving four units to the right on the x-axis and that resulted in y=(x-4)^2. The graph of this equation is in blue.
4. Then I did a reflection across the x-axis and my equation turned up to be y=-x^2. The graph of this equation is in purple.
5. Then I combined my vertical and horizontal translations and so my new equation turned up to be y=(x-4)^2+6. The graph of this equation was in green.
6. Finally I combined my vertical and horixontal translations with my reflection across the x-axis and I got this equation y=-(x-4)^2+6. The graph is in black.
Overall I performed five transformations since I changed the basic function five times and got five differnt equations from the basic function: y=(x-4)^2, y=-x, y=x^2+6, y=(x-4)^2+6, and y=-(x-4)^2+6.
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