Question

Use the table to answer the question. x y −1 2 0 1 1 0 2 1 3 2 Create an absolute value equation based on the table. (1 point) y=|x+blank|

Answer 1

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)**.