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The image shows a table of values for the equation \( y = |x + 2| + 5 \), which needs to be completed.

Let's work through the values for \( y \) based on the given \( x \)-values in the table:

The equation is:
\[
y = |x + 2| + 5
\]
We will plug in each \( x \)-value into the equation and calculate \( y \):

1. For \( x = -5 \):
   \[
   y = |-5 + 2| + 5 = | -3 | + 5 = 3 + 5 = 8
   \]

2. For \( x = -3 \):
   \[
   y = |-3 + 2| + 5 = | -1 | + 5 = 1 + 5 = 6
   \]

3. For \( x = -2 \):
   \[
   y = |-2 + 2| + 5 = | 0 | + 5 = 0 + 5 = 5
   \]

4. For \( x = 0 \):
   \[
   y = |0 + 2| + 5 = | 2 | + 5 = 2 + 5 = 7
   \]

5. For \( x = 3 \):
   \[
   y = |3 + 2| + 5 = | 5 | + 5 = 5 + 5 = 10
   \]

6. For \( x = 5 \):
   \[
   y = |5 + 2| + 5 = | 7 | + 5 = 7 + 5 = 12
   \]

The completed table of values should look like this:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-5 & 8 \\
-3 & 6 \\
-2 & 5 \\
0  & 7 \\
3  & 10 \\
5  & 12 \\
\hline
\end{array}
\]

Would you like help with graphing the equation, or further details on how to interpret the absolute value function?

Here are 5 related questions to consider:
1. How does the absolute value function affect the graph of the equation?
2. What would happen to the table if the equation were \( y = |x - 2| + 5 \)?
3. How do different transformations (e.g., vertical shifts) affect the shape of an absolute value graph?
4. What is the vertex of the graph for \( y = |x + 2| + 5 \)?
5. How does the slope change on either side of the vertex in absolute value functions?

**Tip**: Always double-check your table of values before graphing, as small mistakes in calculations can affect the accuracy of your graph.

Complete the table of values for the equation y = |x + 2| + 5 and then graph the equation.

Learn how to complete a table of values for the absolute value equation y = |x + 2| + 5. This problem demonstrates how to calculate y-values based on given x-values and is suitable for students in Grades 7-9.

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