To find the equation of the new function $g(x)$, we need to apply the described transformations to the original function $f(x) = x^2$.

Steps:

1. Translation to the right by 2 units:

   • Translating a function to the right by $h$ units modifies the function by replacing $x$ with $x - h$. Here, $h = 2$, so the transformation is: $f(x - 2) = (x - 2)^2$

2. Translation up by 5 units:

   • Translating a function up by $k$ units adds $k$ to the entire function. Here, $k = 5$, so the final transformation is: $g(x) = (x - 2)^2 + 5$

Thus, the new equation for $g(x)$ is: $g(x) = (x - 2)^2 + 5$

Answer:

The correct new equation for $g(x)$ is $g(x) = (x - 2)^2 + 5$.

Do you want more details, or do you have any questions?

Here are five related questions:

1. What is the vertex of the parabola $g(x) = (x - 2)^2 + 5$?
2. How does translating a graph left affect the equation?
3. What happens if the parabola $f(x) = x^2$ is reflected over the x-axis?
4. How would the equation change if the graph was moved down by 3 units instead?
5. What is the difference between vertical and horizontal translations?

Tip: When translating a graph horizontally, the transformation affects the $x$-coordinate, while vertical translations modify the $y$-coordinate.