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The graph provided is a parabola that opens downwards, indicating that the coefficient \( a \) of the quadratic function \( y = ax^2 + bx + c \) is negative. 

You are asked to find the value of \( b^2 - 4ac \), which is the discriminant of the quadratic equation. The discriminant tells us about the nature of the roots of the quadratic equation. Here's how the discriminant works:

- \( b^2 - 4ac > 0 \): The equation has two distinct real roots.
- \( b^2 - 4ac = 0 \): The equation has one real root (the vertex touches the x-axis).
- \( b^2 - 4ac < 0 \): The equation has no real roots (the parabola does not touch the x-axis).

In the graph shown, the parabola crosses the x-axis at two points, meaning the quadratic has two distinct real roots. Therefore, \( b^2 - 4ac > 0 \).

Thus, the value of \( b^2 - 4ac \) must be **positive**.

Would you like more details or further clarification?

Here are 5 related questions for further understanding:
1. What happens to the roots if \( b^2 - 4ac \) equals zero?
2. How does the sign of the coefficient \( a \) affect the direction of the parabola?
3. How can we calculate the axis of symmetry for this quadratic function?
4. What role does the discriminant play in solving quadratic equations using the quadratic formula?
5. How would changing the value of \( b \) affect the position of the parabola?

**Tip:** The discriminant not only tells us about the number of roots but also gives insights into the parabola’s intersection with the x-axis, which can be useful in graphing.

Write down the value of b^2 - 4ac from the quadratic equation y = ax^2 + bx + c.

Learn how to calculate the discriminant b^2 - 4ac for a quadratic equation y = ax^2 + bx + c. Understand the significance of the discriminant in determining the nature of roots of the equation. This topic is essential for students learning algebra and quadratic equations, suitable for Grades 9-11.

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