To find [tex]\( g(p) \)[/tex] given the function [tex]\( g(x) = -x^2 + 4x + 4 \)[/tex], we need to substitute [tex]\( p \)[/tex] for [tex]\( x \)[/tex] in the function. Here’s a step-by-step explanation:
1. Write down the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(x) = -x^2 + 4x + 4
\][/tex]
2. Substitute [tex]\( p \)[/tex] into [tex]\( g(x) \)[/tex] to obtain [tex]\( g(p) \)[/tex]:
[tex]\[
g(p) = -(p)^2 + 4(p) + 4
\][/tex]
3. Simplify the expression [tex]\( g(p) \)[/tex]:
[tex]\[
g(p) = -p^2 + 4p + 4
\][/tex]
Thus, the value of [tex]\( g(p) \)[/tex] is:
[tex]\[
g(p) = -p^2 + 4p + 4
\][/tex]
