To solve the problem, we need to evaluate the function $f(x) = -4x^2 + 8x + 11$ at $x = -3$.

Let's substitute $x = -3$ into the function:

$f(-3) = -4(-3)^2 + 8(-3) + 11$

Now, calculate each term:

1. $(-3)^2 = 9$, so $-4(-3)^2 = -4 \times 9 = -36$
2. $8(-3) = -24$
3. The constant term is $11$

Substitute these values back into the function:

$f(-3) = -36 - 24 + 11$

Simplify the expression:

$f(-3) = -60 + 11 = -49$

So, the value of $f(-3)$ is -49.

Would you like more details or have any questions?

Here are some related questions that might interest you:

1. How do you evaluate a function at a different value?
2. What is the significance of finding the value of a function at a specific point?
3. How do you graph a quadratic function like $f(x) = -4x^2 + 8x + 11$?
4. What does the negative coefficient of $x^2$ tell you about the parabola?
5. How do you find the vertex of the quadratic function?

Tip: Remember that substituting values carefully and following the order of operations (PEMDAS) will help avoid mistakes when evaluating functions.