In order to determine which square root equation is represented by the graph, we need to consider the transformations and characteristics of the equations given.
The standard form of a square root function is \( y = a\sqrt{x - h} + k \), where \( (h, k) \) is the vertex of the graph, \( a \) affects the vertical stretch/compression and direction (upward or downward) of the graph.
From the options provided:
- \( y = 2\sqrt{x} - 3 \)
- \( y = 2\sqrt{x} + 6 \)
- \( y = 2\sqrt{x} + 9 \)
- \( y = 2\sqrt{x} - 9 \)
To analyze these options:
- The first and last equations shift the graph downward.
- The second and third equations will shift the graph upward.
To determine which equation matches the graph:
- Check the vertex point (the lowest point of the graph if it opens upward).
- Examine the vertical stretch (the value of \( a \)) to see how quickly the graph rises.
Without the actual graph or more details, I can't definitively tell you which option represents it, but you can determine it by checking which equation aligns with the vertex of the graph you can see.
If the graph moves downwards or shows a specific vertical stretch, refer to the corresponding equations. Please compare the vertex and other characteristics from the graph with these functions.
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