Find the coordinates of the vertex: y=|x+7|+8. Write your answer as an ordered pair (including parentheses).




The vertex is 

The equation you have is \( y = |x + 7| + 8 \), which represents an absolute value function. The vertex of an absolute value function is the point where the expression inside the absolute value equals zero.

### Steps to find the vertex:
1. Set the expression inside the absolute value to zero:
   \[
   x + 7 = 0
   \]
   Solving this gives:
   \[
   x = -7
   \]

2. Now substitute \( x = -7 \) into the equation to find the corresponding \( y \)-coordinate:
   \[
   y = |(-7) + 7| + 8 = 0 + 8 = 8
   \]

Thus, the vertex of the function is at \( (-7, 8) \).

### Final answer:
The vertex is \( (-7, 8) \).

Would you like more details or have any other questions? Here are some related questions for further practice:

1. What is the general form of an absolute value function?
2. How do you find the axis of symmetry for an absolute value function?
3. What is the range of the function \( y = |x + 7| + 8 \)?
4. How would the graph change if the equation were \( y = |x + 7| - 8 \)?
5. Can you describe the graph of the function \( y = |x - 3| + 2 \)?

**Tip**: For an absolute value function \( y = |x - h| + k \), the vertex is always at \( (h, k) \).

Find the coordinates of the vertex: y = |x + 7| + 8. Write your answer as an ordered pair (including parentheses).

Discover how to find the vertex of the absolute value function y = |x + 7| + 8 with a step-by-step solution. This problem covers key algebraic concepts such as absolute value functions and vertex points. Suitable for students in Grades 8-10.

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