The problem involves determining the correct condition for the parameters $a$, $b$, and $c$ of a quadratic function $y = ax^2 + bx + c$, based on the graph shown.

Looking at the graph:

1. The parabola opens downward.
2. The vertex of the parabola is above the x-axis, suggesting that the vertex is a maximum point.

Analyzing the conditions:

• For the parabola to open downward, the coefficient $a$ must be negative.
• Since the vertex is above the x-axis, the value of $c$, which corresponds to the y-intercept, should be positive.
• The coefficient $b$ doesn't directly affect whether the parabola opens upward or downward, but it does influence the position of the vertex along the x-axis.

Conclusion:

• Option B $a < 0, b < 0, c > 0$ is correct.

Would you like a detailed breakdown of why this is the correct choice? Or do you have any further questions?

Additional related questions:

1. What effect does the value of $a$ have on the shape of a parabola?
2. How does the coefficient $b$ affect the location of the vertex of the parabola?
3. What does the value of $c$ represent in the quadratic function and its graph?
4. How do you determine the vertex of a parabola from the quadratic equation?
5. Can a quadratic function have a parabola that opens upward and is also above the x-axis?

Tip: To find the vertex of a parabola given the quadratic equation, you can use the formula $x = \frac{-b}{2a}$ to determine the x-coordinate of the vertex.