State the interval in which the graph is decreasing: 1.(x+4)²+5

The given function is \( f(x) = (x + 4)^2 + 5 \).

### Step-by-Step Solution:

1. **Identify the function type**:  
   This is a quadratic function of the form \( f(x) = a(x + h)^2 + k \), which represents a parabola. The parabola opens upwards because the coefficient of \( (x + 4)^2 \) is positive (1).

2. **Find the vertex**:  
   The vertex of a parabola in the form \( (x + h)^2 + k \) is at \( (-h, k) \). Here, \( h = -4 \) and \( k = 5 \).  
   Therefore, the vertex is at \( (-4, 5) \).

3. **Determine the behavior**:  
   Since the parabola opens upwards, the function decreases to the left of the vertex and increases to the right of the vertex.

4. **State the interval of decreasing**:  
   The graph is decreasing on the interval where \( x < -4 \).

### Final Answer:
The function is decreasing on the interval \( (-\infty, -4) \).

Would you like more details or have any questions? 

Here are 5 related questions for further practice:
1. Find the interval where the function \( f(x) = (x - 3)^2 + 2 \) is increasing.
2. Determine the vertex of the function \( f(x) = (x + 2)^2 - 1 \).
3. What is the axis of symmetry for the function \( f(x) = (x - 5)^2 + 3 \)?
4. Find the range of the function \( f(x) = (x + 1)^2 - 4 \).
5. Determine whether the function \( f(x) = -2(x + 1)^2 + 5 \) is increasing or decreasing.

**Tip**: The vertex of a quadratic function is the key point where the graph changes direction (increases or decreases).

State the interval in which the graph is decreasing: 1. (x+4)²+5

Discover how to find the interval where the function (x + 4)² + 5 decreases. This step-by-step solution covers concepts such as quadratic functions, the vertex theorem, and identifying the interval of a decreasing parabola. Suitable for students in Grades 9-10.

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