What is the transformation from the graph `y=x^{2}` to the graph `y=x^{2}-2`?
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To transform the graph from `y=x^{2}` to `y=x^{2}-2`, we need to shift the entire graph down by 2 units.
1. Start with the graph of `y=x^{2}`.
2. Subtract 2 from every y-coordinate of the graph to shift it down by 2 units.
- The equation `y=x^{2}` becomes `y=x^{2}-2`.
- For example, if the original graph had a point (1, 1), after the transformation, it would become (1, -1).
3. Plot the transformed points to create the new graph `y=x^{2}-2`.
Here is how the original graph `y=x^{2}` (in blue) transforms into the graph `y=x^{2}-2` (in red):
Original Graph: `y=x^{2}`
```
| *
2 | *
| *
1 | *
| *
0 |*
|--------------------------------------
0 1 2 3 4 5 6 7 8 9 10
```
Transformed Graph: `y=x^{2}-2`
```
| *
2 |
|
1 | *
| *
0 | *
| *
-1 |*
|--------------------------------------
0 1 2 3 4 5 6 7 8 9 10
```
As shown, the entire graph of `y=x^{2}` has shifted down by 2 units to form the graph of `y=x^{2}-2`.