The problem asks about transforming a function based on a translation. Specifically, for Question 9:

The given parent function is $f(x) = (x)^2$, and the task is to translate the function 4 units to the right and 3 units down.

Translating a Function:

1. Translation to the right: To translate the graph of a function $f(x)$ to the right by $h$ units, you replace $x$ with $(x - h)$. In this case, $h = 4$, so you replace $x$ with $(x - 4)$.

2. Translation downward: To translate a function downward by $k$ units, you subtract $k$ from the function. Here, $k = 3$, so you subtract 3 from the function.

New Equation:

Combining these transformations, the new equation becomes: $f(x) = (x - 4)^2 - 3$

Let me know if you'd like more details on how transformations work!

Related Questions:

1. What happens to the graph if the function is translated 4 units to the left instead of the right?
2. How does translating a function upward by 3 units affect the equation?
3. What are the effects of reflecting a function about the x-axis?
4. Can you describe the difference between vertical and horizontal stretches of a quadratic function?
5. How does combining shifts and stretches impact the shape of the graph?

Tip:

When working with transformations, always focus on how each shift or stretch modifies the $x$ and $y$ coordinates of key points.