To complete the table of values for the function [tex]\( y = x^2 + 7 \)[/tex], we need to calculate the values of [tex]\( y \)[/tex] for given [tex]\( x \)[/tex] values.
The general form of the function [tex]\( y = x^2 + 7 \)[/tex] is:
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = (-2)^2 + 7 = 4 + 7 = 11
\][/tex]
Hence, [tex]\( A = 11 \)[/tex].
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = (-1)^2 + 7 = 1 + 7 = 8
\][/tex]
As given, [tex]\( y = 8 \)[/tex] for [tex]\( x = -1 \)[/tex].
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 0^2 + 7 = 0 + 7 = 7
\][/tex]
As given, [tex]\( y = 7 \)[/tex] for [tex]\( x = 0 \)[/tex].
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 1^2 + 7 = 1 + 7 = 8
\][/tex]
As given, [tex]\( y = 8 \)[/tex] for [tex]\( x = 1 \)[/tex].
5. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 2^2 + 7 = 4 + 7 = 11
\][/tex]
Hence, [tex]\( B = 11 \)[/tex].
Putting these values into the table, we get:
[tex]\[
\begin{tabular}{c||c|c|c|c|c}
$x$ & -2 & -1 & 0 & 1 & 2 \\
\hline
$y$ & 11 & 8 & 7 & 8 & 11 \\
\end{tabular}
\][/tex]
Therefore, the numbers that replace [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are [tex]\( 11 \)[/tex] and [tex]\( 11 \)[/tex] respectively.
