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The problem provided is a translation (translasi) of the function \( f(x) = 4x^2 - 3x + 6 \) by the vector \( T = \begin{pmatrix} 0 \\ -3 \end{pmatrix} \).

### Translation of Functions:
When a function \( f(x) \) is translated by the vector \( T = \begin{pmatrix} 0 \\ -k \end{pmatrix} \), it means the function is shifted vertically by \( k \). Since the translation vector \( T = \begin{pmatrix} 0 \\ -3 \end{pmatrix} \), the function will shift downward by 3 units.

### How to Apply the Translation:
We simply subtract 3 from the output of the original function \( f(x) \):

\[
f'(x) = f(x) - 3
\]
Substitute the expression for \( f(x) \):
\[
f'(x) = (4x^2 - 3x + 6) - 3
\]
Simplify:
\[
f'(x) = 4x^2 - 3x + 3
\]

### Conclusion:
The translated function is \( f'(x) = 4x^2 - 3x + 3 \).

Would you like more details or have any other questions?

Here are some related questions you might be interested in:
1. How do horizontal translations affect a quadratic function?
2. What are the effects of translating a function by both horizontal and vertical vectors?
3. How do translations differ from reflections or dilations in function transformations?
4. Can translation be represented in terms of matrix operations?
5. How do you determine the vertex of a quadratic function after translation?

**Tip:** When translating a function vertically, focus on adjusting the output of the function, whereas horizontal translations affect the input variable directly.

Fungsi f(x) = 4x^2 - 3x + 6 ditranslasikan oleh T = (0, -3). Hasil translasi fungsi tersebut adalah ...

Explore how the quadratic function f(x) = 4x^2 - 3x + 6 is translated downward by 3 units. This tutorial covers the concept of function translation and how it affects the graph of quadratic equations.

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