To create an absolute value equation based on the values in the table, we can analyze the points provided and identify how they relate to the format \( y = |x + c| \).
Given the points:
- \( (-1, 2) \)
- \( (0, 1) \)
- \( (1, 0) \)
- \( (2, 1) \)
- \( (3, 2) \)
We can see that the \( y \) values decrease to a minimum when \( x = 1 \) (where \( y = 0 \)) and increase symmetrically around this point.
To find \( c \), we note that the vertex of the absolute value function occurs at \( x = 1 \) where \( y = 0 \). Therefore, we can write:
\[ y = |x - 1| \]
As such, the absolute value equation based on the table can be expressed as:
\[ y = |x - 1| \]
So, in the format you provided, it would be:
\[ y = |x + (-1)| \]
Thus, the blank would be \(-1\):
\[ y = |x + (-1)| \]
Final answer: \( y = |x - 1| \) (where the blank is -1).
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