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give me the ponits to plot

To plot the function \( f(x) = 2|x + 2| + 3 \), we'll evaluate it for a few key values of \( x \). This will give us the points we need to graph the function.

### Function Breakdown:
1. \( f(x) = 2|x + 2| + 3 \) means we first compute the absolute value of \( x + 2 \), then multiply that result by 2, and finally add 3.
   
### Sample Points:
Let's compute \( f(x) \) for some values of \( x \).

- For \( x = -4 \):
  \[
  f(-4) = 2|(-4) + 2| + 3 = 2| -2 | + 3 = 2(2) + 3 = 4 + 3 = 7
  \]
  Point: \( (-4, 7) \)

- For \( x = -2 \):
  \[
  f(-2) = 2|(-2) + 2| + 3 = 2|0| + 3 = 2(0) + 3 = 3
  \]
  Point: \( (-2, 3) \)

- For \( x = 0 \):
  \[
  f(0) = 2|(0) + 2| + 3 = 2|2| + 3 = 2(2) + 3 = 4 + 3 = 7
  \]
  Point: \( (0, 7) \)

- For \( x = 2 \):
  \[
  f(2) = 2|(2) + 2| + 3 = 2|4| + 3 = 2(4) + 3 = 8 + 3 = 11
  \]
  Point: \( (2, 11) \)

- For \( x = 4 \):
  \[
  f(4) = 2|(4) + 2| + 3 = 2|6| + 3 = 2(6) + 3 = 12 + 3 = 15
  \]
  Point: \( (4, 15) \)

### Points to Plot:
The points are:
- \( (-4, 7) \)
- \( (-2, 3) \)
- \( (0, 7) \)
- \( (2, 11) \)
- \( (4, 15) \)

These are key points that you can plot on a graph. You'll notice the function has a "V" shape due to the absolute value. 

Would you like me to go into further detail on how to graph it? Or do you have any specific questions? 

### Further Questions:
1. How does the value inside the absolute value affect the graph?
2. What happens if you change the coefficient of the absolute value term?
3. How would the graph change if we had a negative sign before the absolute value?
4. How do you find the vertex of an absolute value function?
5. What are some real-world applications of absolute value functions?

**Tip**: To graph absolute value functions, identify the vertex first, as it gives the "corner" of the V-shape, and then plot points to the left and right for symmetry!

give me the points to plot f(x) = 2|x + 2| + 3

Learn how to graph the absolute value function f(x) = 2|x + 2| + 3 by plotting key points. The function involves transformations of the basic absolute value graph, including a vertical stretch and a horizontal shift. Key points include (-4, 7), (-2, 3), (0, 7), (2, 11), and (4, 15). Suitable for students in Grades 7-9.

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