Question

Rewrite the function f(x)=4(x-3)^2 - 12 in the form f(x)=ax^2 + bx + c

Answer 1

To rewrite the function \( f(x) = 4(x - 3)^2 - 12 \) in the form \( f(x) = ax^2 + bx + c \), we'll start by expanding \( (x - 3)^2 \).

1. Expand \( (x - 3)^2 \):

\[
(x - 3)^2 = x^2 - 6x + 9
\]

2. Substitute this back into the function \( f(x) \):

\[
f(x) = 4(x - 3)^2 - 12 = 4(x^2 - 6x + 9) - 12
\]

3. Distribute the \( 4 \):

\[
f(x) = 4x^2 - 24x + 36 - 12
\]

4. Combine like terms:

\[
f(x) = 4x^2 - 24x + 24
\]

Thus, in the form \( f(x) = ax^2 + bx + c \), we have:

\[
\boxed{f(x) = 4x^2 - 24x + 24}
\]