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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.

Given the parent function f(x) = x^2, what is the new equation if the function is translated 4 units to the right and 3 units down?

Learn how to translate the quadratic function f(x) = x^2 by 4 units to the right and 3 units down. This problem covers key algebraic concepts and demonstrates the impact of horizontal and vertical translations on the equation.

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