To determine the equation of the square root function Rhianna graphed, we have to consider the general form of a square root function, which is typically written as:
\[ y = a \sqrt{x - h} + k \]
where \( (h, k) \) is the vertex of the graph and \( a \) affects the steepness of the curve.
In the provided options, we are looking for a function that fits this general form.
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Analyze the options:
- \( y = 12\sqrt{x - 4} \)
- \( y = \frac{1}{2}\sqrt{x - 4} \)
- \( y = 12\sqrt{x + 4} \)
- \( y = \frac{1}{2}\sqrt{x + 4} \)
- \( y = 2\sqrt{x + 4} \)
- \( y = 2\sqrt{x - 4} \)
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Choose the likely candidate based on \(h\) and \(k\). If the vertex of the graph is at \( (h, k) = (4, 0) \) or \( (4, 4) \), you would be inclined to choose \( x - 4 \) or \( x + 4 \) appropriately.
In this situation, only the equations that include \( \sqrt{x - 4} \) or \( \sqrt{x + 4} \) would be candidates if we know \( h \).
If you are not presented with the graph but need to choose just based on the expressions given:
- Check for valid transformations:
- Of the options available, notice that transformations can be critical.
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Assuming the function opens upwards and is translated correctly, if the vertex is \( (4,0) \) then the correct function would be:
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If focusing primarily on the vertex (4) and seeing a downward or upward movement positively or negatively influences the shape, we'd check \( y = 2\sqrt{x - 4} \) given it likely appears steeper.
Therefore, without additional indication from the graph and purely analyzing function characteristics:
The most likely equation based on standard graph layouts for square root functions and without further qualifiers would be:
y = 2√(x - 4)
If you can see that from the graph \( (h=4,k=0) \), then that would affirm the function's slope as approximate and aligned constructions of the vertex shown.
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