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 $x = 0$.