Write an absolute value function that represents both the table and the graph shown.
 
***xx***

**yy**

2

8

3

6

4

4

5

2

6

0





Write your function in the form y=a|x−h|+ky=a|x−h|+k. Do not include spaces.



y=−2∣x−6∣+0


The given function representing the table and graph is:

\[
y = -2|x - 6| + 0
\]

This is in the form \( y = a|x - h| + k \), where:
- \( a = -2 \) controls the vertical stretch and reflection,
- \( h = 6 \) shifts the graph horizontally to the right,
- \( k = 0 \) shifts the graph vertically, but since it’s 0, there is no vertical shift.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does changing the value of \( a \) affect the shape of the graph?
2. What would happen if \( h \) were negative in the function?
3. Can you identify the vertex of the absolute value graph from the function?
4. How would adding a non-zero \( k \) value shift the graph vertically?
5. How does the absolute value function differ from a quadratic function?

**Tip**: The vertex of an absolute value function in the form \( y = a|x - h| + k \) is always located at \( (h, k) \).

Write an absolute value function that represents both the table and the graph shown.

xx | yy
2  | 8
3  | 6
4  | 4
5  | 2
6  | 0

Write your function in the form y=a|x−h|+k. Do not include spaces.

Learn how to represent a table of values and its corresponding graph using an absolute value function. This problem focuses on function transformations, including vertical stretching, horizontal shifting, and identifying the vertex. Suitable for Grades 8-10 students.

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