Question

Given f, of, x, equals, minus, 4, x, squared, plus, 3, x, minus, 11f(x)=−4x
2
+3x−11, find f, of, minus, 4f(−4)

Answer 1

To find \( f(-4) \) for the function \( f(x) = -4x^2 + 3x - 11 \), we start by substituting \(-4\) into the function.

\[
f(-4) = -4(-4)^2 + 3(-4) - 11
\]

Calculating each term step-by-step:

1. Calculate \((-4)^2\):
\[
(-4)^2 = 16
\]

2. Multiply by \(-4\):
\[
-4 \cdot 16 = -64
\]

3. Calculate \(3(-4)\):
\[
3 \cdot (-4) = -12
\]

Now substitute these values back into \( f(-4) \):

\[
f(-4) = -64 - 12 - 11
\]

Combine the values:

\[
f(-4) = -64 - 12 = -76
\]
\[
f(-4) = -76 - 11 = -87
\]

Thus, \( f(-4) = -87 \).

Now, we need to find \( -4f(-4) \):

\[
-4f(-4) = -4(-87) = 348
\]

Therefore, the final answer is:

\[
\boxed{348}
\]