https://file.aiquickdraw.com/mathbot/file/1727064107559oruuj710.jpg

The problem is asking you to identify the equation of the graph shown, which represents a transformation of a square root function.

The form given is \( y = \pm \sqrt{a x} \), where \( a = \pm 1 \) or \( \pm 2 \).

From observing the graph:
- The graph is reflected across the x-axis, which suggests the negative square root function, meaning it starts from the origin and curves downward. 
- The curve is fairly steep, implying \( a = -2 \), since a larger \( a \) value stretches the graph vertically.

Thus, the equation of the graph appears to be:

\[
y = -\sqrt{2x}
\]

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions for further practice:
1. How would the graph of \( y = \sqrt{2x} \) compare to this one?
2. What happens if \( a \) is positive in the function \( y = \sqrt{a x} \)?
3. How do vertical and horizontal stretches affect the graph of a square root function?
4. What is the domain and range of the graph \( y = -\sqrt{2x} \)?
5. How do you reflect a square root graph over the x-axis and y-axis?

**Tip**: When identifying transformations, always pay attention to reflections (sign changes) and stretches (the value of \( a \)).

The graph shown is a shift, also called a translation, of y = ±√(a x), where a = ±1 or ±2. The graph is y = __.

Learn how to determine the equation of a transformed square root function. This problem covers the reflection and vertical stretch transformations of y = ±√(a x). Suitable for high school students studying algebra.

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