https://file.aiquickdraw.com/mathbot/file/1725333686328e2d0ehe4.jpg

Let's analyze the image and solve the problems indicated.

### Problem 27:
**Given function**: \( f(x) = -2(x+3)^2 + 5 \)

**Instructions**: The problem seems to ask for a description or interpretation of the graph of the given quadratic function.

**Solution**:
1. **Vertex Form**: The function is in vertex form, \( f(x) = a(x-h)^2 + k \), where the vertex is \((h, k)\).
   - Here, \( a = -2 \), \( h = -3 \), and \( k = 5 \).
   - Vertex: \((-3, 5)\).
   
2. **Direction of Opening**:
   - Since \( a = -2 \) is negative, the parabola opens **downward**.
   
3. **Axis of Symmetry**:
   - The axis of symmetry is \( x = -3 \).

4. **Maximum Value**:
   - The maximum value of the function occurs at the vertex, so the maximum value is \( f(-3) = 5 \).

### Problem 55:
**Given function**: The graph appears to be a piecewise function, or the problem asks for identification or interpretation of a graph. Without more details, I'll assume it is a basic graph interpretation.

**Solution**:
1. **Shape of the Graph**:
   - If the graph is a parabola, linear, or absolute value function, identify the key points (vertex, intercepts, etc.).
   - Describe the overall behavior of the graph, such as increasing/decreasing intervals, maximum/minimum points.

Since the details are not fully clear from the image and the specific instructions for Problem 55, I recommend checking the problem number to confirm the exact question. If it's about graph interpretation, you should identify key points and describe the graph's behavior.

Would you like to delve deeper into either problem or have further clarifications?

### Related Questions:
1. How do you find the vertex of a quadratic function in vertex form?
2. What is the significance of the sign of the coefficient \(a\) in a quadratic function?
3. How do you determine the axis of symmetry for a parabola?
4. What is the process to find the maximum or minimum value of a quadratic function?
5. Can you explain how to interpret a piecewise function graph?

### Tip:
When dealing with quadratic functions, always check the coefficient of the squared term to determine the direction in which the parabola opens (upward if positive, downward if negative).

Learn how to solve the arithmetic problem 27 minus 55 with a step-by-step explanation. This problem involves basic subtraction and is suitable for early elementary school students (Grades 1-3).

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