https://file.aiquickdraw.com/mathbot/file/1726971420022a73gg4mv.jpg

The function you need to graph is:

\[
y = 4 \sqrt{x}
\]

This is a square root function that involves scaling the square root by a factor of 4. To graph it correctly, let's start by identifying a few key points to plot:

1. **Starting point (endpoint)**: The square root function \( y = \sqrt{x} \) is defined for \( x \geq 0 \), so the endpoint is at \( (0, 0) \), because \( y = 4 \sqrt{0} = 0 \).

2. **Other points**:
   - When \( x = 1 \), \( y = 4 \sqrt{1} = 4 \).
   - When \( x = 4 \), \( y = 4 \sqrt{4} = 8 \).
   - When \( x = 9 \), \( y = 4 \sqrt{9} = 12 \) (this would be off the graph, but is useful for visualization).

### Key Points to Plot:
- \( (0, 0) \) (the endpoint)
- \( (1, 4) \)
- \( (4, 8) \)

Once you plot these points, you can draw a smooth curve passing through them to represent the graph of \( y = 4 \sqrt{x} \). This function increases slowly at first and then more rapidly as \( x \) increases.

Let me know if you'd like more help or further clarification.

---

Do you have any questions or would you like additional details?  
Here are 5 related questions you might want to explore:

1. How does the coefficient in front of the square root function affect the graph?
2. What would happen if the equation had a negative square root?
3. How does the graph of \( y = \sqrt{x} \) compare to \( y = 4\sqrt{x} \)?
4. What is the domain and range of the function \( y = 4 \sqrt{x} \)?
5. How would you transform the graph if the equation was \( y = 4 \sqrt{x-2} + 3 \)?

**Tip:** For square root functions, the graph is always restricted to values where \( x \geq 0 \), since the square root of negative numbers is not defined in real numbers.

Learn how to graph the square root function y = 4√x with key points like (0,0), (1,4), and (4,8). Understand how the coefficient 4 affects the scaling of the graph. Suitable for students in Grades 9-10 studying algebra and graphing techniques.

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