Certainly! To fill in the values of [tex]\(y\)[/tex] in the table for the given function [tex]\(y = 3x^2 - 4\)[/tex], we will evaluate the function at each specified [tex]\(x\)[/tex] value.
Let's go step by step:
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = 3(-2)^2 - 4
\][/tex]
[tex]\[
y = 3(4) - 4
\][/tex]
[tex]\[
y = 12 - 4
\][/tex]
[tex]\[
y = 8
\][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = 3(-1)^2 - 4
\][/tex]
[tex]\[
y = 3(1) - 4
\][/tex]
[tex]\[
y = -1
\][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 3(0)^2 - 4
\][/tex]
[tex]\[
y = 0 - 4
\][/tex]
[tex]\[
y = -4
\][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 3(1)^2 - 4
\][/tex]
[tex]\[
y = 3(1) - 4
\][/tex]
[tex]\[
y = -1
\][/tex]
5. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 3(2)^2 - 4
\][/tex]
[tex]\[
y = 3(4) - 4
\][/tex]
[tex]\[
y = 12 - 4
\][/tex]
[tex]\[
y = 8
\][/tex]
Now we can fill in the table with the calculated [tex]\(y\)[/tex] values:
[tex]\[
\begin{tabular}{|l|l|l|l|l|l|}
\hline
$x$ & -2 & -1 & 0 & 1 & 2 \\
\hline
$y$ & 8 & -1 & -4 & -1 & 8 \\
\hline
\end{tabular}
\][/tex]
So, the completed table is:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$x$ & -2 & -1 & 0 & 1 & 2 \\
\hline
$y$ & 8 & -1 & -4 & -1 & 8 \\
\hline
\end{tabular}
\][/tex]
