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The problem asks to find the vertex of the quadratic function \( f(x) = -4x^2 + 9x + 11 \) using the vertex formula. 

For a quadratic function in standard form \( f(x) = ax^2 + bx + c \), the x-coordinate of the vertex is given by the formula:

\[
x = \frac{-b}{2a}
\]

In this case:
- \( a = -4 \)
- \( b = 9 \)

Now, let's compute the x-coordinate of the vertex and then plug it into the function to find the y-coordinate.

Let me calculate that for you.The vertex of the quadratic function \( f(x) = -4x^2 + 9x + 11 \) is \( (1.125, 16.0625) \).

Let me know if you would like more details, and feel free to ask any questions.

Here are 5 related questions to consider:
1. How does the vertex formula relate to completing the square?
2. What does the vertex represent in the graph of a quadratic function?
3. How can the vertex be used to determine if the parabola opens upwards or downwards?
4. What is the significance of the y-intercept in this quadratic function?
5. How would the graph change if the quadratic term's coefficient became positive?

**Tip:** The vertex of a parabola is the point where the graph changes direction, and it is either the maximum or minimum point of the function depending on whether it opens upwards or downwards.

Use the quadratic function f(x) = -4x^2 + 9x + 11 to answer the following question: Use the vertex formula to determine the vertex.

Learn how to find the vertex of the quadratic function f(x) = -4x^2 + 9x + 11 using the vertex formula. This problem involves key algebraic concepts such as quadratic equations and the vertex of a parabola. Suitable for students in Grades 9-12.

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