Question

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

Answer 1

To rewrite the function \( f(x) = 4(x - 3)^2 - 12 \) in the standard form \( f(x) = ax^2 + bx + c \), we need to expand the function.

1. Start with the expression:
\[
f(x) = 4(x - 3)^2 - 12
\]

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

3. Substitute this back into the function:
\[
f(x) = 4(x^2 - 6x + 9) - 12
\]

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

5. Combine like terms:
\[
f(x) = 4x^2 - 24x + 24
\]

So, in the form \( f(x) = ax^2 + bx + c \), we have:
\[
a = 4, \quad b = -24, \quad c = 24
\]

Thus, the final form is:
\[
f(x) = 4x^2 - 24x + 24
\]