Question

Given f, of, x, equals, minus, 4, x, squared, plus, 8, x, plus, 11f(x)=−4x
2
+8x+11, find f, of, minus, 3f(−3)

Answer 1

To find \( f(-3) \) for the function \( f(x) = -4x^2 + 8x + 11 \), we'll substitute \( -3 \) into the function.

1. Substitute \( x = -3 \) into the function:
\[
f(-3) = -4(-3)^2 + 8(-3) + 11
\]

2. Calculate \( (-3)^2 \):
\[
(-3)^2 = 9
\]

3. Replace \( (-3)^2 \) in the equation:
\[
f(-3) = -4(9) + 8(-3) + 11
\]

4. Compute \( -4(9) \):
\[
-4(9) = -36
\]

5. Compute \( 8(-3) \):
\[
8(-3) = -24
\]

6. Now substitute back:
\[
f(-3) = -36 - 24 + 11
\]

7. Combine the terms:
\[
f(-3) = -36 - 24 = -60
\]
\[
-60 + 11 = -49
\]

Therefore,
\[
f(-3) = -49.
\]