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To solve this problem, we’ll analyze the graphs given to determine the characteristics of the quadratic equations in the form \( y = ax^2 + bx + c \). Specifically, we need to identify:

1. Whether \( a \) is positive or negative.
2. The value of \( c \), which represents the y-intercept of each graph.

### Analyzing Graph A
1. **Sign of \( a \):** In Graph A, the parabola opens **downward**. This indicates that \( a \) is **negative**.
2. **Value of \( c \):** The y-intercept is the point where the graph crosses the y-axis. In Graph A, the graph crosses the y-axis at \( y = -5 \). Therefore, \( c = -5 \).

So, for Graph A:
- \( a \) is negative.
- \( c = -5 \).

### Analyzing Graph B
1. **Sign of \( a \):** In Graph B, the parabola opens **upward**. This indicates that \( a \) is **positive**.
2. **Value of \( c \):** In Graph B, the graph crosses the y-axis at \( y = 4 \). Thus, \( c = 4 \).

So, for Graph B:
- \( a \) is positive.
- \( c = 4 \).

### Summary of Results
- **Graph A:** \( a \) is negative, \( c = -5 \).
- **Graph B:** \( a \) is positive, \( c = 4 \).

Would you like more details or have any questions?

#### Related Questions
1. How does the value of \( a \) affect the direction of a parabola?
2. How is the vertex of a parabola related to the coefficients \( a \) and \( b \)?
3. How would you find the x-intercepts of these quadratic equations?
4. What would happen to the graphs if the value of \( c \) changed?
5. How can we determine the vertex from the standard form of a quadratic equation?

#### Tip
The value of \( c \) in a quadratic equation \( y = ax^2 + bx + c \) always represents the y-intercept, where the graph crosses the y-axis at \( x = 0 \).

For each graph given, determine whether the coefficient 'a' in the equation y = ax^2 + bx + c is positive or negative, and find the value of c.

Analyze graphs of quadratic functions to determine the sign of the leading coefficient 'a' and identify the y-intercept 'c'. Suitable for students learning about parabolas and quadratic functions.

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