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.