Here are the key calculations for the function \( f(x) = -0.3x^2 + 1.6x + 2 \):

1. **Vertex**: 
   - The x-coordinate of the vertex is approximately \( x = 2.67 \).
   - The y-coordinate of the vertex is approximately \( y = 4.13 \).

   Therefore, the vertex is at \( (2.67, 4.13) \), which represents the **maximum point** of the parabola.

2. **X-intercepts** (roots):
   - The function crosses the x-axis at approximately \( x = -1.05 \) and \( x = 6.38 \).

Would you like more details or further calculations?

Here are some related questions you might explore:

1. How can you express this quadratic function in vertex form?
2. How would you find the axis of symmetry for this function?
3. What is the significance of the x-intercepts in this context?
4. Can you verify the maximum value using the derivative of the function?
5. How would this function's graph change if you altered the coefficients?

**Tip:** The x-intercepts are points where \( f(x) = 0 \). Solving this gives valuable information about the function's roots!

Explore how to solve the quadratic function f(x) = -0.3x^2 + 1.6x + 2, including finding the vertex at (2.67, 4.13) and identifying the x-intercepts. This problem covers important algebraic concepts like parabolas, the vertex formula, and quadratic functions. Suitable for students in Grades 9-12.

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