To complete the table of values for the function [tex]\( y = x^2 - x - 6 \)[/tex], we need to calculate the value of [tex]\( y \)[/tex] for each given [tex]\( x \)[/tex] value in the table.
Here are the steps for each calculation:
1. When [tex]\( x = -3 \)[/tex]:
[tex]\[
y = (-3)^2 - (-3) - 6 = 9 + 3 - 6 = 6
\][/tex]
So, [tex]\( y = 6 \)[/tex].
2. When [tex]\( x = -2 \)[/tex]:
[tex]\[
y = (-2)^2 - (-2) - 6 = 4 + 2 - 6 = 0
\][/tex]
So, [tex]\( y = 0 \)[/tex].
3. When [tex]\( x = -1 \)[/tex]:
[tex]\[
y = (-1)^2 - (-1) - 6 = 1 + 1 - 6 = -4
\][/tex]
So, [tex]\( y = -4 \)[/tex].
4. When [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 0^2 - 0 - 6 = -6
\][/tex]
So, [tex]\( y = -6 \)[/tex].
5. When [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 1^2 - 1 - 6 = 1 - 1 - 6 = -6
\][/tex]
So, [tex]\( y = -6 \)[/tex].
6. When [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 2^2 - 2 - 6 = 4 - 2 - 6 = -4
\][/tex]
So, [tex]\( y = -4 \)[/tex].
Now, let's update the table with the corrected values of [tex]\( y \)[/tex]:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$x$ & -3 & -2 & -1 & 0 & 1 & 2 \\
\hline
$y$ & 6 & 0 & -4 & -6 & -6 & -4 \\
\hline
\end{tabular}
\][/tex]
