Let's determine the missing [tex]\( y \)[/tex] values for the given [tex]\( x \)[/tex] values using the function [tex]\( y = x^2 - 3 \)[/tex]. We need to fill in the entries of the table.
Given:
[tex]\[ y = x^2 - 3 \][/tex]
We are provided with:
[tex]\[\begin{array}{|c|c|c|c|c|c|}
\hline
x & -5 & -3 & 0 & 1 & 2 \\
\hline
y & \text{?} & \text{?} & \text{?} & 1 & 13 \\
\hline
\end{array}\][/tex]
### Step-by-Step Solution:
1. For [tex]\( x = -5 \)[/tex]:
[tex]\[ y = (-5)^2 - 3 \][/tex]
[tex]\[ y = 25 - 3 \][/tex]
[tex]\[ y = 22 \][/tex]
Therefore:
[tex]\[ y = 22 \][/tex]
2. For [tex]\( x = -3 \)[/tex]:
[tex]\[ y = (-3)^2 - 3 \][/tex]
[tex]\[ y = 9 - 3 \][/tex]
[tex]\[ y = 6 \][/tex]
Therefore:
[tex]\[ y = 6 \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = (0)^2 - 3 \][/tex]
[tex]\[ y = 0 - 3 \][/tex]
[tex]\[ y = -3 \][/tex]
Therefore:
[tex]\[ y = -3 \][/tex]
### Final Table:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -5 & -3 & 0 & 1 & 2 \\
\hline
y & 22 & 6 & -3 & 1 & 13 \\
\hline
\end{array}
\][/tex]
Thus, the completed table is:
[tex]\[
\begin{array}{| c | c | c | c | c | c |}
\hline
x & -5 & -3 & 0 & 1 & 2 \\
\hline
y & 22 & 6 & -3 & 1 & 13 \\
\hline
\end{array}
\][/tex]
