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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