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The image shows a question related to the translation of a function. The problem is to determine the translation matrix \( T \) that transforms the quadratic function:

\[
y = 2x^2 - x + 3
\]

into:

\[
y = 2x^2 - x - 5
\]

### Explanation:

In a translation transformation, only the constant term of the function changes, while the terms involving \( x \) and \( x^2 \) remain unchanged. Here, we observe that the function has been transformed from having a constant term of \( +3 \) to \( -5 \). 

This means the translation corresponds to the change in the constant term, which is:

\[
\Delta y = -5 - 3 = -8
\]

Therefore, the translation in the \( y \)-direction is \( -8 \), while there is no change in the \( x \)-direction, so \( \Delta x = 0 \).

Thus, the translation matrix \( T \) is:

\[
T = \begin{pmatrix} 0 \\ -8 \end{pmatrix}
\]

### The correct option:
The correct answer is **c.**

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### Related Questions:
1. How do you find the translation matrix for other types of functions?
2. What is the general form of a translation matrix in two dimensions?
3. Can translation transformations be combined with other types of transformations like rotations or reflections?
4. How do translations affect the graph of a quadratic function?
5. What is the significance of the translation vector in geometrical transformations?

### Tip:
In any translation, remember that only the position of the graph shifts while the shape remains unchanged. The shift is entirely described by the change in the constant term of the equation.

Bentuk translasi transformasi y = 2x^2 - x + 3 menjadi y = 2x^2 - x - 5 adalah...

Learn how to determine the translation matrix that transforms the quadratic function y = 2x^2 - x + 3 into y = 2x^2 - x - 5. This problem demonstrates how translation affects only the constant term in a quadratic function and how to calculate the translation vector. Suitable for students in Grades 9-11.

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