To convert the function [tex]\( f(x) = 4(x + 6)^2 + 5 \)[/tex] into its standard form [tex]\( f(x) = ax^2 + bx + c \)[/tex], let's follow the steps of expanding and simplifying the given expression.
1. Expand the binomial:
[tex]\[
(x + 6)^2 = x^2 + 12x + 36
\][/tex]
2. Multiply the binomial term by 4:
[tex]\[
4(x^2 + 12x + 36) = 4x^2 + 48x + 144
\][/tex]
3. Add the constant 5:
[tex]\[
4x^2 + 48x + 144 + 5 = 4x^2 + 48x + 149
\][/tex]
The standard form of the function is:
[tex]\[
f(x) = 4x^2 + 48x + 149
\][/tex]
Thus, the coefficients are:
[tex]\[
a = 4, \quad b = 48, \quad c = 149
\][/tex]
