Question

Given f, of, x, equals, minus, 3, x, squared, plus, 6, x, plus, 1f(x)=−3x
2
+6x+1, find f, of, 6f(6)

Answer 1

To find \( f(6) \) given the function \( f(x) = -3x^2 + 6x + 1 \), we simply need to substitute \( x = 6 \) into the function.

So, let's calculate \( f(6) \):

\[
f(6) = -3(6^2) + 6(6) + 1
\]

Calculating \( 6^2 \):

\[
6^2 = 36
\]

Now substitute this into the equation:

\[
f(6) = -3(36) + 6(6) + 1
\]

Calculating the terms:

\[
-3(36) = -108
\]
\[
6(6) = 36
\]

Now combine the results:

\[
f(6) = -108 + 36 + 1
\]

Now, calculate:

\[
-108 + 36 = -72
\]
\[
-72 + 1 = -71
\]

Thus:

\[
f(6) = -71
\]

So the value of \( f(6) \) is \( -71 \).