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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.

Learn how to evaluate the quadratic function f(x) = -4x^2 + 8x + 11 at x = -3. This detailed solution explains how to substitute the value of x and simplify the expression, suitable for students in Grades 9-10.

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