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To solve this problem, let's analyze each quadratic function provided and match it with its corresponding graph by identifying key features, particularly the y-intercept and the direction of the parabola.

### Step 1: Identify Functions
The given functions are:
1. \( f(x) = x^2 + 8x + 15 \)
2. \( f(x) = x^2 - 8x + 15 \)
3. \( f(x) = x^2 + 2x - 15 \)
4. \( f(x) = x^2 - 2x - 15 \)

### Step 2: Analyze Each Function
Each function is a quadratic equation in the form \( f(x) = ax^2 + bx + c \). Key features we can derive from these are:
- **Y-intercept**: This is the constant term \( c \) in the function.
- **Vertex and Direction**: Since all of these have \( a = 1 \), they open upwards. We can complete the square or use the formula for the vertex to find the turning points, or observe transformations.

1. **\( f(x) = x^2 + 8x + 15 \)**
   - Y-intercept: \( 15 \)
   - Vertex: Completing the square or using the vertex formula \( x = -\frac{b}{2a} \), we find \( x = -4 \).
   - Substitute \( x = -4 \) back into the function to find the minimum y-value (vertex).

2. **\( f(x) = x^2 - 8x + 15 \)**
   - Y-intercept: \( 15 \)
   - Vertex: \( x = 4 \)
   - Substitute \( x = 4 \) to find the vertex.

3. **\( f(x) = x^2 + 2x - 15 \)**
   - Y-intercept: \( -15 \)
   - Vertex: \( x = -1 \)

4. **\( f(x) = x^2 - 2x - 15 \)**
   - Y-intercept: \( -15 \)
   - Vertex: \( x = 1 \)

### Step 3: Match to Graphs
Using the information derived, we can then match each function to its graph based on the vertex, y-intercept, and shape.

Would you like a breakdown of the calculations for each function's vertex, or do you have any specific questions on how to proceed? 

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Here are 5 related questions that build on this topic:

1. How can you determine the vertex of a quadratic function without completing the square?
2. What does the coefficient of \( x^2 \) tell us about the shape and direction of a parabola?
3. How does changing the constant term in a quadratic function affect its graph?
4. How can you quickly identify the y-intercept from the standard form of a quadratic equation?
5. How does the sign of the coefficient of \( x \) affect the position of the vertex along the x-axis?

**Tip:** Remember, for any quadratic function \( f(x) = ax^2 + bx + c \), the vertex x-coordinate is always given by \( x = -\frac{b}{2a} \).

Match each function with its graph:
Given functions:
1. f(x) = x^2 + 8x + 15
2. f(x) = x^2 - 8x + 15
3. f(x) = x^2 + 2x - 15
4. f(x) = x^2 - 2x - 15

Match these with the correct graphs based on vertex, y-intercept, and parabola direction.

Learn to match quadratic functions like f(x) = x^2 + 8x + 15 with their graphs by analyzing vertices and y-intercepts. This problem provides a practical approach to graphing parabolas and understanding their properties, ideal for Grades 9-10.

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