To evaluate the function [tex]\( g(x) = -2x^2 + 3x - 5 \)[/tex] for the input values [tex]\(-2\)[/tex], [tex]\(0\)[/tex], and [tex]\(3\)[/tex], we follow these steps:
1. Evaluate [tex]\( g(-2) \)[/tex]:
[tex]\[
\begin{array}{l}
g(-2) = -2(-2)^2 + 3(-2) - 5 \\
g(-2) = -2(4) + (-6) - 5 \\
g(-2) = -8 - 6 - 5 \\
g(-2) = -19
\end{array}
\][/tex]
2. Evaluate [tex]\( g(0) \)[/tex]:
[tex]\[
\begin{array}{l}
g(0) = -2(0)^2 + 3(0) - 5 \\
g(0) = 0 + 0 - 5 \\
g(0) = -5
\end{array}
\][/tex]
3. Evaluate [tex]\( g(3) \)[/tex]:
[tex]\[
\begin{array}{l}
g(3) = -2(3)^2 + 3(3) - 5 \\
g(3) = -2(9) + 9 - 5 \\
g(3) = -18 + 9 - 5 \\
g(3) = -14
\end{array}
\][/tex]
Thus, the evaluated values are:
[tex]\[
g(-2) = -19,\, g(0) = -5,\, g(3) = -14
\][/tex]
So in the format that the question asks for, we fill in the squares as follows:
[tex]\[
\begin{array}{l}
g(-2) = -19 \\
g(0) = -5 \\
g(3) = -14
\end{array}
\][/tex]
