The equation \( y = -3|2x| + 4 \) describes a V-shaped graph due to the absolute value function. Here’s how to analyze it:

1. **Vertex**: The vertex occurs when \( |2x| = 0 \), which happens at \( x = 0 \). Plugging this into the equation gives:
   \[
   y = -3|2(0)| + 4 = 4
   \]
   So the vertex is at \( (0, 4) \).

2. **Direction**: Since the coefficient of the absolute value is negative (\(-3\)), the graph opens downwards.

3. **Intercepts**:
   - **Y-intercept**: Set \( x = 0 \):
     \[
     y = 4
     \]
   - **X-intercepts**: Set \( y = 0 \):
     \[
     0 = -3|2x| + 4 \implies -3|2x| = -4 \implies |2x| = \frac{4}{3}
     \]
     This gives:
     \[
     2x = \frac{4}{3} \quad \text{or} \quad 2x = -\frac{4}{3}
     \]
     Thus:
     \[
     x = \frac{2}{3} \quad \text{or} \quad x = -\frac{2}{3}
     \]

4. **Slope**: The slopes of the lines forming the V shape are:
   - Left side (for \( x < 0 \)): slope = \( -3 \times -2 = 6 \)
   - Right side (for \( x > 0 \)): slope = \( -3 \times 2 = -6 \)

### Summary
- **Vertex**: \( (0, 4) \)
- **Y-intercept**: \( (0, 4) \)
- **X-intercepts**: \( \left( \frac{2}{3}, 0 \right) \) and \( \left( -\frac{2}{3}, 0 \right) \)
- **Opens Downward** with slopes of 6 (left) and -6 (right).

Would you like more details or have any specific questions about this function? Here are some follow-up questions you might consider:

1. How do changes in the coefficients affect the graph?
2. Can you explain the concept of absolute value functions?
3. What would happen if we added a constant to this equation?
4. How do you find the domain and range of this function?
5. What is the significance of the vertex in the context of this graph?

**Tip**: Always sketch the graph to visualize the properties of the function effectively!

Explore the graph of the function y = -3|2x| + 4. This resource provides insights into its vertex, intercepts, and slopes, making it suitable for students in Grades 8-10 learning about absolute value functions.

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