https://file.aiquickdraw.com/mathbot/file/1725937149253rabv9g07.jpg

Let's analyze the graph and the equations shown.

1. The first equation is \( y = \sqrt{x} + 8 \). This represents a transformation of the parent function \( y = \sqrt{x} \), which is shifted 8 units upwards. In the graph, the **green** curve is the one that is shifted the highest, corresponding to this equation. Therefore, the correct answer for the first question is **green**.

2. The second equation is \( y = \sqrt{x} - 2 \). This is also a transformation of \( y = \sqrt{x} \), but it is shifted 2 units downward. The **blue** curve is the one that is shifted downward, indicating it matches this equation. Thus, the correct answer for the second question is **blue**.

Would you like a detailed explanation of graph transformations or have any other questions? Here are some related questions:

1. What are the general rules for vertical shifts in function transformations?
2. How does the graph of \( y = \sqrt{x} \) differ from other parent functions?
3. Can horizontal shifts affect the graph similarly to vertical shifts?
4. How can the domain and range of \( y = \sqrt{x} + 8 \) be determined?
5. What happens when both horizontal and vertical shifts are applied to \( y = \sqrt{x} \)?

**Tip:** When graphing, vertical shifts are controlled by constants added or subtracted outside the function (e.g., \( y = f(x) + c \)), while horizontal shifts are caused by changes inside the function (e.g., \( y = f(x - h) \)).

What color graph will have the equation y = √x + 8? What color graph will have the equation y = √x - 2?

Understand how to identify the correct color graph for the equations y = √x + 8 and y = √x - 2 through graph transformations. This problem explores vertical shifts in square root functions, perfect for students in Grades 9-10.

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