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 \( \square \).

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).**