Use transformations to explain how the graph of $$ f $$ can be found by using the graph of $$ y=x^{2} $$. $$ f(x)=(x-5)^{2}+4 $$ Which of the following explains the transformations to find the graph of $$ f $$ ? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. Shifting the graph of $$ y=x^{2} $$ to the right $$ \square $$ units then vertically shifting the graph up $$ \square $$ unit(s). B. Shifting the graph of $$ y=x^{2} $$ to the left $$ \square $$ units then vertically shifting the graph down $$ \square $$ unit(s). Chifting of $$ y=x^{2} $$ to the left $$ \square $$ units and then horizontally shrinking the resulting graph by a factor of $$ \square $$. Shifting of $$ y=x^{2} $$ to the left $$ \square $$ units and then vertically stretching the resulting graph by a factor of $$ \square $$.

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To find the graph of $$ f(x) = (x-5)^{2} + 4 $$ using the graph of $$ y = x^{2} $$, we can analyze the transformations step by step.

1. **Identify the transformations**:
   - The expression $$ (x-5)^{2} $$ indicates a horizontal shift.
   - The $$ +4 $$ indicates a vertical shift.

2. **Horizontal Shift**:
   - The term $$ (x-5) $$ means we shift the graph of $$ y = x^{2} $$ to the right by 5 units. This is because subtracting a number inside the function (i.e., $$ x - 5 $$) results in a rightward shift.

3. **Vertical Shift**:
   - The $$ +4 $$ means we shift the graph vertically upwards by 4 units.

Now, we can fill in the blanks based on our analysis:

- The graph of $$ y = x^{2} $$ is shifted to the right **5** units.
- Then, it is vertically shifted up **4** units.

Thus, the correct choice is:

**A. Shifting the graph of $$ y=x^{2} $$ to the right $$ 5 $$ units then vertically shifting the graph up $$ 4 $$ unit(s).**
To graph $$ f(x) = (x-5)^{2} + 4 $$ using $$ y = x^{2} $$, shift the graph right by 5 units and up by 4 units. **A. Shifting the graph of $$ y=x^{2} $$ to the right 5 units then vertically shifting the graph up 4 unit(s).**

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