What transformations change the graph of \( f(x) \) to the graph of \( g(x) \) ? \( f(x)=x^{2} g(x)=(x+5)^{2}+5 \) a The graph of \( g(x) \) is the graph of \( f(x) \) translated to the down 5 units and right 5 units. o o The graph of \( g(x) \) is the graph of \( f(x) \) translated to the left 5 units and up 5 units. d the graph of \( g(x) \) is the graph of \( f(x) \) translated to the right 5 units and down 5 units.

To determine the transformations that change the graph of \( f(x) = x^2 \) to the graph of \( g(x) = (x + 5)^2 + 5 \), we can analyze the changes made to the function. 1. **Starting with \( f(x) = x^2 \)**: - This is a standard parabola that opens upwards with its vertex at the origin (0, 0). 2. **Analyzing \( g(x) = (x + 5)^2 + 5 \)**: - The term \( (x + 5)^2 \) indicates a horizontal shift. Specifically, it shifts the graph to the left by 5 units (since we replace \( x \) with \( x + 5 \)). - The \( +5 \) outside the square indicates a vertical shift. This shifts the graph up by 5 units. 3. **Combining the transformations**: - The graph of \( g(x) \) is obtained by first shifting the graph of \( f(x) \) to the left by 5 units and then shifting it up by 5 units. Thus, the correct transformation is: - The graph of \( g(x) \) is the graph of \( f(x) \) translated to the left 5 units and up 5 units. So the answer is: **The graph of \( g(x) \) is the graph of \( f(x) \) translated to the left 5 units and up 5 units.**