https://file.aiquickdraw.com/mathbot/file/1726017529832zsm80f25.jpg

The problem shown in the image is about determining the translation (translasi) of a quadratic function.

We are given two equations:

1. \( y = 2x^2 - x + 3 \)
2. \( y = 2x^2 - x - 5 \)

To find the transformation that has occurred, we compare the two equations. The only difference is the constant term:

- In the first equation, the constant is \( +3 \).
- In the second equation, the constant is \( -5 \).

This change represents a **vertical translation**. Specifically, the function has been shifted downwards by \( 3 - (-5) = 8 \) units.

Thus, the transformation is a **vertical translation of 8 units downwards**.

Would you like more details or have any questions?

Here are some related questions to further explore the concept:

1. How do you determine the direction of translation in a quadratic function?
2. What effect does a change in the \(x\)-coefficient have on the graph of a quadratic function?
3. How can you find horizontal translations in functions?
4. What is the vertex form of a quadratic function and how does it help in identifying transformations?
5. How does the leading coefficient of a quadratic function affect its graph?

**Tip**: To analyze transformations, always compare the coefficients of corresponding terms, including constants, to detect shifts and stretches.

Bentuk translasinya dari y = 2x^2 - x + 3 menjadi y = 2x^2 - x - 5 adalah ....

Learn how to identify vertical translations in quadratic functions with a detailed explanation. In this problem, we examine the transformation of y = 2x^2 - x + 3 to y = 2x^2 - x - 5, resulting in a vertical shift of 8 units downwards. Suitable for Grades 9-10.

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